This paper studies the use of vector Lyapunov functions for the design of
globally stabilizing feedback laws for nonlinear systems. Recent results on
vector Lyapunov functions are utilized. The main result of the paper shows that
the existence of a vector control Lyapunov function is a necessary and
sufficient condition for the existence of a smooth globally stabilizing
feedback. Applications to nonlinear systems are provided: simple and easily
checkable sufficient conditions are proposed to guarantee the existence of a
smooth globally stabilizing feedback law.

The mathematical methods underlying a recent quantum feedback experiment
stabilizing photon-number states is developed. It considers a controlled system
whose quantum state, a finite dimensional density operator, is governed by a
discrete-time nonlinear Markov process. In open-loop, the measurements are
assumed to be quantum non-demolition (QND) measurements.

We study the situation of an investor-producer who can trade on a financial
market in continuous time and can transform some assets into others by means of
a discrete time production system, in order to price and hedge derivatives on
produced goods. This general framework covers the interesting case of an
electricity producer who wants to hedge a financial position and can trade
commodities which are also inputs for his system. This extends the framework of
Bouchard and Nguyen (2011) to continuous time for concave and bounded
production functions.

We focus here on the analysis of the regularity or singularity of solutions
$\Om_{0}$ to shape optimization problems among convex planar sets, namely: $$
J(\Om_{0})=\min\{J(\Om),\ \Om\ \textrm{convex},\ \Omega\in\mathcal S_{ad}\}, $$
where $\mathcal S_{ad}$ is a set of 2-dimensional admissible shapes and
$J:\mathcal{S}_{ad}\rightarrow\R$ is a shape functional. Our main goal is to
obtain qualitative properties of these optimal shapes by using first and second
order optimality conditions, including the infinite dimensional Lagrange
multiplier due to the convexity constraint.

Pathwise predictability and predictors are studied in deterministic setting
for discrete time processes. A family of one step predictor is suggested for
processes with energy decay on higher frequencies. For these processes, the
prediction error can be made arbitrarily small.

Pathwise predictability and predictors for discrete time processes are
studied in deterministic setting. More precisely, we suggest predictors based
on approximation of convolution sums over future times by convolution sums over
past time. These predictors are such that all band-limited processes are
predictable in this sense, as well as high-frequency processes with zero energy
at low frequencies. It follows that a process of mixed type still can be
predicted if an ideal low-pass filter exists for this process.

We study causal dynamic approximation of non-bandlimited processes by
band-limited processes such that a part of the historical path of the
underlying process is approximated in $L_2$-norm by the trace of a band-limited
process. This allows to cover the case of irregular non-smooth processes. We
show that this problem has an unique optimal solution. The approximating
band-limited process is obtained in time domain in a form of sinc series. To
accommodate the current flow of observations, the coefficients of this series
and the related band-limited process have to be changed dynamically.

We provide bounds on the error between dynamics of an infinite dimensional
bilinear Schr\"odinger equation and of its finite dimensional Galerkin
approximations. Standard averaging methods are used on the finite dimensional
approximations to obtain constructive controllability results. As an
illustration, the methods are applied on a model of a 2D rotating molecule.

This paper develops sufficient conditions for the existence of global
exponential observers for two classes of nonlinear systems: (i) the class of
systems with a globally asymptotically stable compact set, and (ii) the class
of systems that evolve on an open set. In the first class, the derived
continuous-time observer also leads to the construction of a robust global
sampled-data exponential observer, under additional conditions.

In this note, we examine the problem of identifying the interaction geometry
among a known number of agents, adopting a consensus-type algorithm for their
coordination. The proposed identification process is facilitated by introducing
"ports" for stimulating a subset of network vertices via an appropriately
defined interface and observing the network's response at another set of
vertices.

We consider problems of estimation of structured covariance matrices, and in
particular of matrices with a Toeplitz structure. We follow a geometric
viewpoint that is based on some suitable notion of distance. To this end, we
overview and compare several alternatives metrics and divergence measures. We
advocate a specific one which represents the Wasserstein distance between the
corresponding Gaussians distributions and show that it coincides with the
so-called Bures/Hellinger distance between covariance matrices as well.

We consider an inventory system in which inventory level fluctuates as a
Brownian motion in the absence of control. The inventory continuously
accumulates cost at a rate that is a general convex function of the inventory
level, which can be negative when there is a backlog. At any time, the
inventory level can be adjusted by a positive or negative amount, which incurs
a fixed cost and a proportional cost. The challenge is to find an adjustment
policy that balances the holding cost and adjustment cost to minimize the
long-run average cost.

The minimum time function $T(\cdot)$ of smooth control systems is known to be
locally semiconcave provided Petrov's controllability condition is satisfied.
Moreover, such a regularity holds up to the boundary of the target under an
inner ball assumption. We generalize this analysis to differential inclusions,
replacing the above hypotheses with the continuity of $T(\cdot)$ near the
target, and an inner ball property for the multifunction associated with the
dynamics. In such a weakened set-up, we prove that the hypograph of $T(\cdot)$
satisfies, locally, an exterior sphere condition.

Large outliers break down linear and nonlinear regression models. Robust
regression methods allow one to filter out the outliers when building a model.
By replacing the traditional least squares criterion with the least trimmed
squares criterion, in which half of data is treated as potential outliers, one
can fit accurate regression models to strongly contaminated data.
High-breakdown methods have become very well established in linear regression,
but have started being applied for non-linear regression only recently.

We propose in this paper a gradient-type dynamical system to solve the
problem of maximizing quantum observables for finite dimensional closed quantum
ensembles governed by the controlled Liouville-von Neumann equation. The
asymptotic behavior is analyzed: we show that under the regularity assumption
on the controls the dynamical system almost always converges to a solution of
the maximization problem; we also detail the difficulties related to the
occurrence of singular controls.

Optimal power flow (OPF) is an important problem for power generation and it
is in general non-convex. With the employment of renewable energy, it will be
desirable if OPF can be solved very efficiently so its solution can be used in
real time. With some special network structure, e.g. trees, the problem has
been shown to have a zero duality gap and the convex dual problem yields the
optimal solution. In this paper, we propose a primal and a dual algorithm to
coordinate the smaller subproblems decomposed from the convexified OPF.

We generalize the fractional Caputo derivative to the fractional derivative
${{^CD}^{\alpha,\beta}_{\gamma}}$, which is a convex combination of the left
Caputo fractional derivative of order $\alpha$ and the right Caputo fractional
derivative of order $\beta$. The fractional variational problems under our
consideration are formulated in terms of ${{^CD}^{\alpha,\beta}_{\gamma}}$. The
Euler-Lagrange equations for the basic and isoperimetric problems, as well as
transversality conditions, are proved.

X-ray crystallography and nuclear magnetic resonance (NMR) spectroscopy are
two powerful tools to determine the protein 3D structure. However, not all
proteins can be successfully crystallized, particularly for membrane proteins.
Although NMR spectroscopy is indeed very powerful in determining the 3D
structures of membrane proteins, same as X-ray crystallography, it is still
very time-consuming and expensive. Under many circumstances, due to the
noncrystalline and insoluble nature of some proteins, X-ray and NMR cannot be
used at all.

Within the unmanageably large class of nonconvex optimization, we consider
the rich subclass of nonsmooth problems that have \emph{composite}
objectives---this already includes the extensively studied convex, composite
objective problems as a special case. For this subclass, we introduce a
powerful, new framework that permits asymptotically \emph{non-vanishing}
perturbations. In particular, we develop perturbation-based batch and
incremental (online like) nonconvex proximal splitting algorithms.

We introduce a data-driven order reduction method for nonlinear control
systems, drawing on recent progress in machine learning and statistical
dimensionality reduction. The method rests on the assumption that the nonlinear
system behaves linearly when lifted into a high (or infinite) dimensional
feature space where balanced truncation may be carried out implicitly.

This paper investigates the necessary conditions of optimality for uni-
formly overtaking optimal control on infinite horizon with free right endpoint.
Clarke's form of the Pontryagin Maximum Principle is proved without the as-
sumption on boundedness of total variation of adjoint variable. The
transversality condition for adjoint variable is shown to become necessary if
the adjoint variable is partially Lyapunov stable. The modifications of this
condition are proposed for the case of unbounded adjoint variable. The
Cauchy-type formula for the adjoint variable proposed by S. M.

The asymptotic behavior of stochastic gradient algorithms is studied. Relying
on results from differential geometry (Lojasiewicz gradient inequality), the
single limit-point convergence of the algorithm iterates is demonstrated and
relatively tight bounds on the convergence rate are derived. In sharp contrast
to the existing asymptotic results, the new results presented here do not
require the objective function to have an isolated minimum and to be strongly
convex in an open vicinity of that minimum.

In this paper we develop a randomized block-coordinate descent method for
minimizing the sum of a smooth and a simple nonsmooth block-separable convex
function and prove that it obtains an $\epsilon$-accurate solution with
probability at least $1-\rho$ in at most $O(\tfrac{n}{\epsilon} \log
\tfrac{1}{\rho})$ iterations, where $n$ is the number of blocks. For strongly
convex functions the method converges linearly.

In a continuous time stochastic economy, this paper considers the problem of
consumption and investment in a financial market in which the representative
investor exhibits a change in the discount rate. The investment opportunities
are a stock and a riskless account. The market coefficients and discount factor
switches according to a finite state Markov chain. The change in the discount
rate leads to time inconsistencies of the investor's decisions. The randomness
in our model is driven by a Brownian motion and Markov chain.

In this paper, we consider a control synthesis problem for a class of
polynomial dynamical systems subject to bounded disturbances and with input
constraints. More precisely, we aim at synthesizing at the same time a
controller and an invariant set for the controlled system under all admissible
disturbances. We propose a computational method to solve this problem.

A two-person zero-sum differential game with unbounded controls is
considered. Under proper coercivity conditions, the upper and lower value
functions are characterized as the unique viscosity solutions to the
corresponding upper and lower Hamilton--Jacobi--Isaacs equations, respectively.
Consequently, when the Isaacs' condition is satisfied, the upper and lower
value functions coincide, leading to the existence of the value function.

In this paper we intend to give some calculus rules for tangent sets in the
sense of Bouligand and Ursescu, as well as for corresponding derivatives of
set-valued maps. Both first and second order objects are envisaged and the
assumptions we impose in order to get the calculus are in terms of metric
subregularity of the assembly of the initial data. This approach is different
from those used in alternative recent papers in literature and allows us to
avoid compactness conditions.

This article studies the sensitivity of the power utility maximization
problem with respect to the investor's relative risk aversion, the statistical
probability measure, the investment constraints and the market price of risk.
We extend previous descriptions of the dual domain then exploit the link
between the constrained utility maximization problem and continuous
semimartingale quadratic BSDEs to reduce questions on sensitivity to results on
stability for such equations.

Using ergodic theory, in this paper we present a Gel'fand-type spectral
radius formula which states that the joint spectral radius is equal to the
generalized spectral radius for a matrix multiplicative semigroup $\bS^+$
restricted to a subset that need not carry the algebraic structure of $\bS^+$.
This generalizes the Berger-Wang formula. Using it as a tool, we study the
absolute exponential stability of a linear switched system driven by a compact
subshift of the one-sided Markov shift associated to $\bS$.

In the Multi-Armed Bandit (MAB) problem, there are a given set of arms with
unknown reward distributions. At each time, a player selects one arm to play,
aiming to maximize the total expected reward over a horizon of length T. The
essence of the problem is the tradeoff between exploration and exploitation:
playing a less explored arm to learn its reward statistics for future benefit
or playing the arm with the largest sample mean at the current time.

We show a simple method for constructing an infinite family of graph
formation games with link bias so that the resulting games admits, as a
\textit{pairwise stable} solution, a graph with an arbitrarily specified degree
distribution. Pairwise stability is used as the equilibrium condition over the
more commonly used Nash equilibrium to prevent the occurrence of ill-behaved
equilibrium strategies that do not occur in ordinary play. We construct this
family of games by solving an integer programming problem whose constraints
enforce the terminal pairwise stability property we desire.

As an alternative view to the graph formation models in the statistical
physics community, we introduce graph formation models using \textit{network
formation} through selfish competition as an approach to modeling graphs with
particular topologies. We further investigate a specific application of our
results to collaborative oligopolies. We extend the results of Goyal and Joshi
(S. Goyal and S. Joshi. Networks of collaboration in oligopoly.

This brief presents a simple derivation of the standard model-free control
for the non-minimum phase systems. The robustness of the proposed method is
studied in simulation considering the case of switched systems.

Here, necessary optimal condition for Optimistic Bilevel programming problem
is obtained in Asplund spaces. Also we have got necessary optimal conditions in
finite dimensional spaces, by assuming differentiability on the given
functions.

This paper explores the role of symmetries and reduction in the Pontryagin
maximum principle for optimal control of nonlinear control systems. We first
formulate symmetries in nonlinear control systems and then link them to the
corresponding symmetries in optimal control of such systems. A symmetry in an
optimal control system gives rise to a natural choice of a principal connection
in this setting. We then apply reduction theory of Hamiltonian mechanics to the
Pontryagin maximum principle to reduce the optimal control system; the
principal connection plays a central role here.

In many real world problems, control decisions have to be made with limited
information. The controller may have no a priori (or even posteriori) data on
the nonlinear system, except from a limited number of points that are obtained
over time. This is either due to high cost of observation or the highly
non-stationary nature of the system.

We provide a dynamic programming principle for stochastic optimal control
problems with expectation constraints. A weak formulation, using test functions
and a probabilistic relaxation of the constraint, avoids restrictions related
to a measurable selection but still implies the Hamilton-Jacobi-Bellman
equation in the viscosity sense. We treat open state constraints as a special
case of expectation constraints and prove a comparison theorem to obtain the
equation for closed state constraints.

We consider the symmetric Darlington synthesis of a p x p rational symmetric
Schur function S with the constraint that the extension is of size 2p x 2p.
Under the assumption that S is strictly contractive in at least one point of
the imaginary axis, we determine the minimal McMillan degree of the extension.
In particular, we show that it is generically given by the number of zeros of
odd multiplicity of I-SS*. A constructive characterization of all such
extensions is provided in terms of a symmetric realization of S and of the
outer spectral factor of I-SS*.

The goal of the Machine Learning and Traveling Repairman Problem (ML&TRP) is
to determine a route for a "repair crew," which repairs nodes on a graph. The
repair crew aims to minimize the cost of failures at the nodes, but as in many
real situations, the failure probabilities are not known and must be estimated.
We introduce two formulations for the ML&TRP, where the first formulation is
sequential: failure probabilities are estimated at each node, and then a
weighted version of the traveling repairman problem is used to construct the
route from the failure cost.

This paper presents a detailed proof for the triality theorem in a class of
global optimization problems.

We describe an elementary algorithm to build convex inner approximations of
nonconvex sets. Both input and output sets are basic semialgebraic sets given
as lists of defining multivariate polynomials. Even though no optimality
guarantees can be given (e.g. in terms of volume maximization for bounded
sets), the algorithm is designed to preserve convex boundaries as much as
possible, while removing regions with concave boundaries. In particular, the
algorithm leaves invariant a given convex set.

We propose and analyze an extremely fast, efficient, and simple method for
solving the problem:min{parallel to u parallel to(1) : Au = f, u is an element
of R-n}.This method was first described in [J. Darbon and S. Osher, preprint,
2007], with more details in [W. Yin, S. Osher, D. Goldfarb and J. Darbon, SIAM
J. Imaging Sciences, 1(1), 143-168, 2008] and rigorous theory given in [J. Cai,
S. Osher and Z. Shen, Math. Comp., to appear, 2008, see also UCLA CAM Report
08-06] and [J. Cai, S. Osher and Z. Shen, UCLA CAM Report, 08-52, 2008].

We analyze convergence rates of stochastic optimization procedures for
non-smooth convex optimization problems. By combining randomized smoothing
techniques with accelerated gradient methods, we obtain optimal variance-based
convergence rates of stochastic optimization procedures, both in expectation
and with high probability, To the best of our knowledge, these are the first
variance-based rates for non-smooth optimization.

In this paper, Lipschitz univariate constrained global optimization problems
where both the objective function and constraints can be multiextremal are
considered. The constrained problem is reduced to a discontinuous unconstrained
problem by the index scheme without introducing additional parameters or
variables. A Branch-and-Bound method that does not use derivatives for solving
the reduced problem is proposed. The method either determines the infeasibility
of the original problem or finds lower and upper bounds for the global
solution.

We consider the inverse optimization problem associated with the polynomial
program f^*=\min \{f(x): x\in K\}$ and a given current feasible solution $y\in
K$. We provide a systematic numerical scheme to compute an inverse optimal
solution.

This paper considers the problem of throughput optimal routing/scheduling in
a multi-hop constrained queueing network with random connectivity whose special
case includes opportunistic multi-hop wireless networks and input-queued switch
fabrics. The main challenge in the design of throughput optimal routing
policies is closely related to identifying appropriate and universal Lyapunov
functions with negative expected drift.

Dengue is one of the major international public health concerns. Although
progress is underway, developing a vaccine against the disease is challenging.
Thus, the main approach to fight the disease is vector control. A model for the
transmission of Dengue disease is presented. It consists of eight mutually
exclusive compartments representing the human and vector dynamics. It also
includes a control parameter (insecticide) in order to fight the mosquito. The
model presents three possible equilibria: two disease-free equilibria (DFE) and
another endemic equilibrium.

In this paper we study the semi-global (approximate) state feedback
stabilization of an infinite dimensional quantum stochastic system towards a
target state. A discrete-time Markov chain on an infinite-dimensional Hilbert
space is used to model the dynamics of a quantum optical cavity. We can choose
an (unbounded) strict Lyapunov function that is minimized at each time-step in
order to prove (weak-$\ast$) convergence of probability measures to a final
state that is concentrated on the target state with (a pre-specified)
probability that may be made arbitrarily close to 1.

In this article we study the frictionless cooling of atoms trapped in a
harmonic potential, while minimizing the transient energy of the system. We
show that in the case of unbounded control, this goal is achieved by a singular
control, which is also the time-minimal solution for a "dual" problem, where
the energy is held fixed. In addition, we examine briefly how the solution is
modified when there are bounds on the control.

A risk-neutral method is always used to price and hedge contingent claims in
complete market, but another method based on utility maximization or risk
minimization is wildly used in more general case. One can find all kinds of
special risk measure in literature. In this paper, instead of using market
modified risk measure, we use a kind of risk measure induced by
g_\Gamma-solution or the minimal solution of a Constrained Backward Stochastic
Differential Equation (CBSDE) directly when constraints on wealth and portfolio
process comes to our consideration.

This paper considers the mean variance portfolio management problem. We
examine portfolios which contain both primary and derivative securities. The
challenge in this context is the well posedness of the optimization problem. We
find examples in which this problem is well posed. Numerical experiments
provide the efficient frontier. The methodology developed in this paper can be
also applied to pricing and hedging in incomplete markets.

This paper investigates dividend optimization of an insurance corporation
under a more realistic model which takes into consideration refinancing or
capital injections. The model follows the compound Poisson framework with
credit interest for positive reserve, and debit interest for negative reserve.
Ruin occurs when the reserve drops below the critical value. The company
controls the dividend pay-out dynamically with the objective to maximize the
expected total discounted dividends until ruin.

A discussion of the robustness properties of the proposed observer with
respect to measurement errors is provided for the recently proposed full-order
and reduced-order, hybrid, dead-beat observer for a class of nonlinear systems,
linear in the unmeasured states.

Inhomogeneity, in its many forms, appears frequently in practical physical
systems. Readily apparent in quantum systems, inhomogeneity is caused by
hardware imperfections, measurement inaccuracies, and environmental variations,
and subsequently limits the performance and efficiency achievable in current
experiments. In this paper, we provide a systematic methodology to
mathematically characterize and optimally manipulate inhomogeneous ensembles
with concepts taken from ensemble control.

We consider decentralized restless multi-armed bandit problems with unknown
dynamics and multiple players. The reward state of each arm transits according
to an unknown Markovian rule when it is played and evolves according to an
arbitrary unknown random process when it is passive. Players activating the
same arm at the same time collide and suffer from reward loss. The objective is
to maximize the long-term reward by designing a decentralized arm selection
policy to address unknown reward models and collisions among players.

In this paper, we introduce a class of indicators that enable to compute
efficiently optimal transport plans associated to arbitrary distributions of N
demands and M supplies in R in the case where the cost function is concave. The
computational cost of these indicators is small and independent of N. A
hierarchical use of them enables to obtain an efficient algorithm.

We give a proper fractional extension of the classical calculus of variations
by considering variational functionals with a Lagrangian depending on a
combined Caputo fractional derivative and the classical derivative.
Euler-Lagrange equations to the basic and isoperimetric problems are proved, as
well as transversality conditions.

We consider optimizing average queueing delay and average power consumption
in a nonpreemptive multi-class M/G/1 queue with dynamic power control that
affects instantaneous service rates. Four problems are studied: (1) satisfying
per-class average delay constraints; (2) minimizing a separable convex function
of average delays subject to per-class delay constraints; (3) minimizing
average power consumption subject to per-class delay constraints; (4)
minimizing a separable convex function of average delays subject to an average
power constraint.

A new metaheuristic optimisation algorithm, called Cuckoo Search (CS), was
developed recently by Yang and Deb (2009). This paper presents a more extensive
comparison study using some standard test functions and newly designed
stochastic test functions. We then apply the CS algorithm to solve engineering
design optimisation problems, including the design of springs and welded beam
structures. The optimal solutions obtained by CS are far better than the best
solutions obtained by an efficient particle swarm optimiser.

We investigate the problem of designing delay-aware joint flow control,
routing, and scheduling algorithms in general multi-hop networks for maximizing
network utilization. Since the end-to-end delay performance has a complex
dependence on the high-order statistics of cross-layer algorithms, earlier
optimization-based design methodologies that optimize the long term network
utilization are not immediately well-suited for delay-aware design.

The structural properties of graphs are usually characterized in terms of
invariants, which are functions of graphs that do not depend on the labeling of
the nodes. In this paper we study convex graph invariants, which are graph
invariants that are convex functions of the adjacency matrix of a graph. Some
examples include functions of a graph such as the maximum degree, the MAXCUT
value (and its semidefinite relaxation), and spectral invariants such as the
sum of the $k$ largest eigenvalues.

Bayesian networks are basic graphical models, used widely both in statistics
and artificial intelligence. These statistical models of conditional
independence structure are described by acyclic directed graphs whose nodes
correspond to (random) variables in consideration. A quite important topic is
the learning of Bayesian network structures, which is determining the best
fitting statistical model on the basis of given data.

The principle underlying this paper is the basic observation that the problem
of simultaneously solving a large class of composite monotone inclusions and
their duals can be reduced to that of finding a zero of the sum of a maximally
monotone operator and a linear skew-adjoint operator. An algorithmic framework
is developed for solving this generic problem in a Hilbert space setting. New
primal-dual splitting algorithms are derived from this framework for inclusions
involving composite monotone operators, and convergence results are
established.

In the classic Bayesian restless multi-armed bandit (RMAB) problem, there are
$N$ arms, with rewards on all arms evolving at each time as Markov chains with
known parameters. A player seeks to activate $K \geq 1$ arms at each time in
order to maximize the expected total reward obtained over multiple plays. RMAB
is a challenging problem that is known to be PSPACE-hard in general. We
consider in this work the even harder non-Bayesian RMAB, in which the
parameters of the Markov chain are assumed to be unknown \emph{a priori}.

In this paper we study the generalized version of weighted matching in
bipartite networks. Consider a weighted matching in a bipartite network in
which the nodes derive value from the split of the matching edge assigned to
them if they are matched. The value a node derives from the split depends both
on the split as well as the partner the node is matched to. We assume that the
value of a split to the node is continuous and strictly increasing in the part
of the split assigned to the node.

A novel tracking paradigm for flying geometric shapes using tethered kites is
presented. Because of the one-to-one correspondence between turning angles and
images of curves on a sphere it is possible to fly a given shape by tracking
the associated turning angle. Based on this principle a Lyapunov-based
nonlinear adaptive control loop is developed that needs control derivatives of
the kite aerodynamic model only. The resulting controller is found to be robust
when simulating against the Leuven-Heidelberg rigid body kite model, even under
severe initial model mismatch.

In this paper the problem of stabilizing large-scale systems by distributed
controllers where the controllers exchange information via a shared limited
communication medium is addressed. An event-triggered sampling scheme is
proposed, in which each system decides when to transmit new information across
the network based on the crossing of some error threshold. Stability of the
interconnected large-scale system is inferred by applying a generalized
small-gain theorem.

It is known that state-dependent, multi-step Lyapunov bounds lead to greatly
simplified verification theorems for stability, for large classes of Markov
chain models --- This is one component of the ``fluid model'' approach to
stability of stochastic networks. In this paper we extend the general theory to
randomized multi-step Lyapunov theory to obtain criteria for the existence of a
finite steady state, as well as finite moments.

This paper illustrates the application of recent research in
region-of-attraction analysis for nonlinear hybrid limit cycles. Three example
systems are analyzed in detail: the van der Pol oscillator, the "rimless
wheel", and the "compass gait", the latter two being simplified models of
underactuated walking robots. The method used involves decomposition of the
dynamics about the target cycle into tangential and transverse components, and
a search for a Lyapunov function in the transverse dynamics using
sum-of-squares analysis (semidefinite programming).

A convex set with nonempty interior is maximal lattice-free if it is
inclusion-maximal with respect to the property of not containing integer points
in its interior. Maximal lattice-free convex sets are known to be polyhedra.
The precision of a rational polyhedron $P$ in $\mathbb{R}^d$ is the smallest
integer $s$ such that $sP$ is an integral polyhedron.

A zero-sum differential game with controlled jump-diffusion driven state is
considered, and studied using a combination of dynamic programming and
viscosity solution techniques. We prove, under certain conditions, that the
value of the game exists and is the unique viscosity solution of a fully
nonlinear integro-partial differential equation. In addition, we formulate and
prove a verification theorem for such games within the viscosity solution
framework for nonlocal equations

Performance analysis of queueing networks is one of the most challenging
areas of queueing theory. Barring very specialized models such as product-form
type queueing networks, there exist very few results which provide provable
non-asymptotic upper and lower bounds on key performance measures. In this
paper we propose a new performance analysis method, which is based on the
robust optimization. The basic premise of our approach is as follows: rather
than assuming that the stochastic primitives of a queueing model satisfy
certain probability laws, such as, for example, i.i.d.

This paper develops a general framework for solving a variety of convex cone
problems that frequently arise in signal processing, machine learning,
statistics, and other fields. The approach works as follows: first, determine a
conic formulation of the problem; second, determine its dual; third, apply
smoothing; and fourth, solve using an optimal first-order method. A merit of
this approach is its flexibility: for example, all compressed sensing problems
can be solved via this approach.

A new framework for nonlinear system identification is presented in terms of
optimal fitting of stable nonlinear state space equations to input/output/state
data, with a performance objective defined as a measure of robustness of the
simulation error with respect to equation errors. Basic definitions and
analytical results are presented. The utility of the method is illustrated on a
simple simulation example as well as experimental recordings from a live
neuron.

We consider a zero-sum stochastic differential controller-and-stopper game in
which the state process is a controlled jump-diffusion evolving in a
multi-dimensional Euclidean space. In this game, the controller affects both
the drift and the volatility terms of the state process. Under appropriate
conditions, we show that the lower value function of this game is a viscosity
solution to an obstacle problem for a Hamilton-Jacobi-Bellman equation, by
generalizing the weak dynamic programming principles in [3].

In this paper we consider general rank minimization problems with rank
appearing in either objective function or constraint. We first show that a
class of matrix optimization problems can be solved as lower dimensional vector
optimization problems. As a consequence, we establish that a class of rank
minimization problems have closed form solutions. Using this result, we then
propose penalty decomposition methods for general rank minimization problems in
which each subproblem is solved by a block coordinate descend method.

We study the stochastic control problem of maximizing expected utility from
terminal wealth under a non-bankruptcy constraint. The wealth process is
subject to shocks produced by a general marked point process. The problem of
the agent is to derive the optimal insurance strategy which allows "lowering"
the level of the shocks. This optimization problem is related to a suitable
dual stochastic control problem in which the delicate boundary constraints
disappear.

We consider a dynamic vehicle routing problem in wireless networks where
messages arriving randomly in time and space are collected by a mobile receiver
(vehicle or a collector). The collector is responsible for receiving these
messages via wireless communication by dynamically adjusting its position in
the network. Our goal is to utilize a combination of wireless transmission and
controlled mobility to improve the delay performance in such networks.

We consider a utility maximization problem over partially observable Markov
ON/OFF channels. In this network instantaneous channel states are never known,
and at most one user is selected for service in every slot according to the
partial channel information provided by past observations. Solving the utility
maximization problem directly is difficult because it involves solving
partially observable Markov decision processes. Instead, we construct an
approximate solution by optimizing the network utility only over a good
constrained network capacity region rendered by stationary policies.

We consider the k-disjoint-clique problem. The input is an undirected graph G
in which the nodes represent data items, and edges indicate a similarity
between the corresponding items. The problem is to find within the graph k
disjoint cliques that cover the maximum number of nodes of G. This problem may
be understood as a general way to pose the classical `clustering' problem. In
clustering, one is given data items and a distance function, and one wishes to
partition the data into disjoint clusters of data items, such that the items in
each cluster are close to each other.

We study problems of the calculus of variations and optimal control within
the framework of time scales. Specifically, we obtain Euler-Lagrange type
equations for both Lagrangians depending on higher order delta derivatives and
isoperimetric problems. We also develop some direct methods to solve certain
classes of variational problems via dynamic inequalities. In the last chapter
we introduce fractional difference operators and propose a new discrete-time
fractional calculus of variations.

Supervisory control of discrete-event systems with a global safety
specification and with only local supervisors is a difficult problem. For
global specifications the equivalent conditions for local control synthesis to
equal global control synthesis may not be met. This paper formulates and solves
a control synthesis problem for a generator with a global specification and
with a combination of a coordinator and local controllers. Conditional
controllability is proven to be an equivalent condition for the existence of
such a coordinated controller.

In this paper, the problem of allocating users to radio resources (i.e.,
subcarriers) in the downlink of an OFDMA cellular network is addressed. We
consider a multi-cellular environment with a realistic interference model and a
margin adaptive approach, i.e., we aim at minimizing total transmission power
while maintaining a certain given rate for each user.

This is an short overview of the recent tendencies in the theory of linear
inequalities that are evoked by Boolean valued analysis.

We study continuous time Bertrand oligopolies in which a small number of
firms producing similar goods compete with one another by setting prices. We
first analyze a static version of this game in order to better understand the
strategies played in the dynamic setting. Within the static game, we
characterize the Nash equilibrium when there are $N$ players with heterogeneous
costs. In the dynamic game with uncertain market demand, firms of different
sizes have different lifetime capacities which deplete over time according to
the market demand for their good.

This is a survey on the computational complexity of nonlinear mixed-integer
optimization. It highlights a selection of important topics, ranging from
incomputability results that arise from number theory and logic, to recently
obtained fully polynomial time approximation schemes in fixed dimension, and to
strongly polynomial-time algorithms for special cases.

We present a faster exponential-time algorithm for integer optimization over
quasi-convex polynomials. We study the minimization of a quasi-convex
polynomial subject to s quasi-convex polynomial constraints and integrality
constraints for all variables. The new algorithm is an improvement upon the
best known algorithm due to Heinz (Journal of Complexity, 2005). A lower time
complexity is reached through applying a stronger ellipsoid rounding method and
applying a recent advancement in the shortest vector problem to give a smaller
exponential-time complexity of a Lenstra-type algorithm.

We present an application of optimal control theory to Dengue epidemics. This
epidemiologic disease is an important theme in tropical countries due to the
growing number of infected individuals. The dynamic model is described by a set
of nonlinear ordinary differential equations, that depend on the dynamic of the
Dengue mosquito, the number of infected individuals, and the people's
motivation to combat the mosquito. The cost functional depends not only on the
costs of medical treatment of the infected people but also on the costs related
to educational and sanitary campaigns.

We consider a population of identical individuals preying on an exhaustible
resource. The individuals in the population choose a strategy that defines how
they use their available time over the course of their life for feeding, for
reproducing (say laying eggs), or split their energy in between these two
activities. We here suppose that their life lasts a full season, so that the
chosen strategy results in the production of a certain number of eggs laid over
the season.

We consider switched systems on Banach and Hilbert spaces governed by
strongly continuous one-parameter semigroups of linear evolution operators. We
provide necessary and sufficient conditions for their global exponential
stability, uniform with respect to the switching signal, in terms of the
existence of a Lyapunov function common to all modes.

A mixed type dual to a nondifferentiable variational problem involving higher
order derivative is formulated and duality results are proved under generalized
invexity conditions. Special cases are generated from our results.

An efficient gradient-based method to solve the volume constrained topology
optimization problems is presented. Each iterate of this algorithm is obtained
by the projection of a Barzilai-Borwein step onto the feasible set consisting
of box and one linear constraints (volume constraint). To ensure the global
convergence, an adaptive nonmonotone line search is performed along the
direction that is given by the current and projection point.

We analyze a power distribution line with high penetration of distributed
generation and strong variations of power consumption and generation levels. In
the presence of uncertainty the statistical description of the system is
required to assess the risks of power outages. In order to find the probability
of exceeding the constraints for voltage levels we introduce the probability
distribution of maximal voltage drop and propose an algorithm for finding this
distribution. The algorithm is based on the assumption of random but
statistically independent distribution of loads on buses.

Stability is arguably one of the core concepts upon which our understanding
of dynamical and control systems has been built. The related notion of
incremental stability, however, has received much less attention until
recently, when it was successfully used as a tool for the analysis and design
of intrinsic observers, output regulation of nonlinear systems, frequency
estimators, synchronization of coupled identical dynamical systems, symbolic
models for nonlinear control systems, and bio-molecular systems.

Many of the physical phenomena are second order in nature. Since most of the
physical phenomena are governed by partial differential equations (PDEs), this
makes sense to pose the control on the second order derivatives of PDE's
solutions (in addition to zeros and first order ones) to consistently control
the real-world problems. However, this type of control is theoretically very
difficult and to the best of our knowledge there is nigher a theoretic work nor
a numeric work in literature in this regard.

This work deals with the existence of optimal solution and the maximum
principle for optimal control problem governed by Navier-Stokes equations with
state constraint in 3-D. Strong results in 2-D also are given.

Some nonlinear extensions of the vector maximality statement established by
Goepfert, Tammer and Zalinescu [Nonl. Anal., 39 (2000), 909-922] are given.
Basic instruments for these are the Brezis-Browder ordering principle [Advances
Math., 21 (1976), 355-364] and its logical equivalent in Turinici [Libertas
Math., 20 (2000), 161-172].

With this note we bring again into attention a vector dual problem neglected
by the contributions who have recently announced the successful healing of the
trouble encountered by the classical duals to the classical linear vector
optimization problem. This vector dual problem has, different to the mentioned
works which are of set-valued nature, a vector objective function. Weak, strong
and converse duality for this "new-old" vector dual problem are proven and we
also investigate its connections to other vector duals considered in the same
framework in the literature.

The goal of this paper is to provide an analysis of the "toolkit" method used
in the numerical approximation of the time-dependent Schr\"odinger equation.
The "toolkit" method is based on precomputation of elementary propagators and
was seen to be very efficient in the optimal control framework. Our analysis
shows that this method provides better results than the second order Strang
operator splitting. In addition, we present two improvements of the method in
the limit of low and large intensity control fields.

We study the design of media streaming applications in the presence of
multiple heterogeneous wireless access methods with different throughputs and
costs. Our objective is to analytically characterize the trade-off between the
usage cost and the Quality of user Experience (QoE), which is represented by
the probability of interruption in media playback and the initial waiting time.
We model each access network as a server that provides packets to the user
according to a Poisson process with a certain rate and cost.

This paper considers robust filtering for a nominal Gaussian state-space
model, when an incremental relative entropy tolerance is applied to each
dynamical model component. The problem is formulated as a dynamic minimax game
which is shown to admit a saddle point. The structure of the saddle point is
characterized by applying and extending results presented earlier in [1] for
static least-squares estimation.

We propose an optimization approach to design cost-effective electrical power
transmission networks. That is, we aim to select both the network structure and
the line conductances (line sizes) so as to optimize the trade-off between
network efficiency (low power dissipation within the transmission network) and
the cost to build the network. We begin with a convex optimization method based
on the paper "Minimizing Effective Resistance of a Graph" [Ghosh, Boyd &
Saberi]. We show that this (DC) resistive network method can be adapted to the
context of AC power flow.

The routing capacity region of networks with multiple unicast sessions can be
characterized using Farkas' lemma as an infinite set of linear inequalities. In
this paper this result is sharpened by exploiting properties of the solution
satisfied by each rate-tuple on the boundary of the capacity region, and a
finite description of the routing capacity region which depends on network
parameters is offered. For the special case of undirected ring networks
additional results on the complexity of the description are provided.

We consider the problem of controlling marginally stable linear systems using
bounded control inputs for networked control settings in which the
communication channel between the remote controller and the system is
unreliable. We assume that the states are perfectly observed, but the control
inputs are transmitted over a noisy communication channel. Under mild
hypotheses on the noise introduced by the control communication channel and
large enough control authority, we construct a control policy that renders the
state of the closed-loop system mean-square bounded.

In recent years we have witnessed a move of the major industrial automation
providers into the wireless domain. While most of these companies already offer
wireless products for measurement and monitoring purposes, the ultimate goal is
to be able to close feedback loops over wireless networks interconnecting
sensors, computation devices, and actuators. In this paper we present a
decentralized event-triggered implementation, over sensor/actuator networks, of
centralized nonlinear controllers.

We consider the general bilinear control systems in three-dimensional
Euclidean space which satisfy the LARC and have an open control set U; and give
sufficient controllability conditions for corresponding projected systems on
two-dimensional sphere.

The article introduces a new mechanism for selecting individuals to a Pareto
archive. It was combined with a micro-genetic algorithm and tested on several
problems. The ability of this approach to produce individuals uniformly
distributed along the Pareto set without negative impact on convergence is
demonstrated on presented results. The new concept was confronted with NSGA-II,
SPEA2, and IBEA algorithms from the PISA package. Another studied effect is the
size of population versus number of generations for small populations.

Two-dimensional almost-Riemannian structures are generalized Riemannian
structures on surfaces for which a local orthonormal frame is given by a Lie
bracket generating pair of vector fields that can become collinear. We consider
the Carnot--Caratheodory distance canonically associated with an
almost-Riemannian structure and study the problem of Lipschitz equivalence
between two such distances on the same compact oriented surface.

The detailed mathematical model of heat and mass transfer of steel ingot of
curvilinear continuous casting machine is proposed. The process of heat and
mass transfer is described by nonlinear partial differential equations of
parabolic type. Position of phase boundary is determined by Stefan conditions.
The temperature of cooling water in mould channel is described by a special
balance equation.

We investigate systems of equations, involving parameters from the point of
view of both control theory and computer algebra. The equations might involve
linear operators such as partial (q-)differentiation, (q-)shift, (q-)difference
as well as more complicated ones, which act trivially on the parameters. Such a
system can be identified algebraically with a certain left module over a
non-commutative algebra, where the operators commute with the parameters. We
develop, implement and use in practice the algorithm for revealing all the
expressions in parameters, for which e.g.

Given a compactly supported probability measure on Euclidean space, we study
the asymptotic speed at which it can be approximated (in Wasserstein distance
of any exponent p) by finitely supported measure. When p=1, this is the
location problem and precise asymptotics where given by Bouchitt\'e, Jimenez
and Rajesh. When p=2, this problem is linked with Centroidal Voronoi
Tessellations.

A numerical study of an algorithm proposed by Gusein Guseinov, which
determines approximations to the optimal solution of problems of calculus of
variations using two discretizations and correspondent Euler-Lagrange
equations, is investigated. The results we obtain to discretizations of the
brachistochrone problem and Mania example with Lavrentiev's phenomenon are
compared with the solutions found by other methods and solvers. We conclude
that Guseinov's method presents better solutions in most of the cases studied.

From this set of procedures for given clause we shall choose only
interrogation of experts on pairs decisions. It is widely widespread method. It
makes the whole chapter in the theory of the decision-making, well investigated
with the formal point of view. In the modern theory of decision-making at
gathering the initial information for mathematical model it practically does
not have alternative.

It is introduced the using of generation lexicographical procedure for
multicriteria decision-making problems.

A new concept called "Model-Free Control" is applied to hydroelectric
run-of-the river power plants, with severe constraints and operating
conditions. Numerous computer simulations display excellent results, which are
obtained thanks to simple and robust algorithms.

We prove an abstract Nyquist criterion in a general set up. As applications,
we recover various versions of the Nyquist criterion, some of which are new.

New trajectory-based small-gain results are obtained for nonlinear feedback
systems under relaxed assumptions. Specifically, during a transient period, the
solutions of the feedback system may not satisfy some key inequalities that
previous small-gain results usually utilize to prove stability properties. The
results allow the application of the small-gain perspective to various systems
which satisfy less demanding stability notions than the Input-to-Output
Stability property.

This paper describes a state estimation approach for systems described by
non-causal time-varying uncertain linear descriptor equations with
set-membership description of uncertainty. The approach is based on the notion
a linear minimax estimation.

This paper presents a method to solve the Hamilton-Jacobi-Bellman equation
for a class of second order optimal control problems for which the cost is
quadratic and the dynamics are affine in the input and in the state directly
excited by that input. The solution is based on the concept of inverse
optimality and is obtained in two steps. First a scalar problem is solved and
then the solution of the second order problem is obtained from the solution to
the scalar problem by the addition of a viscous damping term.

We come up with a class of distributed quantized averaging algorithms on
asynchronous communication networks with fixed, switching and random
topologies. The implementation of these algorithms is subject to the realistic
constraint that the communication rate, the memory capacities of agents and the
computation precision are finite. The focus of this paper is on the study of
the convergence time of the proposed quantized averaging algorithms. By
appealing to random walks on graphs, we derive polynomial bounds on the
expected convergence time of the algorithms presented.

For a semialgebraic set K in R^n, let P_d(K) be the cone of polynomials in
R^n of degrees at most d that are nonnegative on K. This paper studies the
geometry of its boundary. When K=R^n and d is even, we show that its boundary
lies on the irreducible hypersurface defined by the discriminant of a single
polynomial. When K is a real algebraic variety, we show that P_d(K) lies on the
hypersurface defined by the discriminant of several polynomials. When K is a
general semialgebraic set, we show that P_d(K) lies on a union of hypersurfaces
defined by the discriminantal equations.