Donald Goldfarb
Structured Sparsity via Alternating Direction Methods.
Fri, 12/16/2011 - 15:01 — SomNambulAuthors: Donald Goldfarb, Zhiwei Qin
Subjects: Optimization and Control
AbstractWe consider a class of sparse learning problems in high dimensional feature
space regularized by a structured sparsity-inducing norm which incorporates
prior knowledge of the group structure of the features. Such problems often
pose a considerable challenge to optimization algorithms due to the
non-smoothness and non-separability of the regularization term. In this paper,
we focus on two commonly adopted sparsity-inducing regularization terms, the
overlapping Group Lasso penalty $l_1/l_2$-norm and the $l_1/l_\infty$-norm.- Read more
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Sparse Inverse Covariance Selection via Alternating Linearization Methods.
Tue, 11/02/2010 - 16:01 — SomNambulAuthors: Donald Goldfarb, Shiqian Ma, Katya Scheinberg
Subjects: Learning
AbstractGaussian graphical models are of great interest in statistical learning.
Because the conditional independencies between different nodes correspond to
zero entries in the inverse covariance matrix of the Gaussian distribution, one
can learn the structure of the graph by estimating a sparse inverse covariance
matrix from sample data, by solving a convex maximum likelihood problem with an
$\ell_1$-regularization term.Fast Alternating Linearization Methods for Minimizing the Sum of Two Convex Functions.
Thu, 12/24/2009 - 16:01 — SomNambulAuthors: Donald Goldfarb, Shiqian Ma
Subjects: Optimization and Control
AbstractSplitting and alternating direction methods have been widely used for solving
convex optimization problems. We present in this paper two first-order
alternating linearization algorithms based on variable splitting and
alternating linearization techniques for minimizing the sum of two convex
functions. We prove that the number of iterations needed by the first algorithm
is $O(1/\epsilon)$ to obtain an $\epsilon$-optimal solution.Fast Multiple Splitting Algorithms for Convex Optimization.
Thu, 12/24/2009 - 16:01 — SomNambulAuthors: Donald Goldfarb, Shiqian Ma
Subjects: Optimization and Control
AbstractWe present in this paper two different classes of general $K$-splitting
algorithms for solving convex optimization problems. We prove that the number
of iterations needed by the first class of algorithms to obtain an
$\epsilon$-optimal solution is $O(1/\epsilon)$. The algorithms in the second
class are accelerated versions of those in the first class, where the
complexity result is improved to $O(1/\sqrt{\epsilon})$ while the computational
effort required at each iteration is almost unchanged.
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