Hongchao Zhang
A nonmonotone spectral projected gradient method for large-scale topology optimization problems.
Fri, 06/04/2010 - 15:01 — SomNambulAuthors: Hongchao Zhang, Ruhollah Tavakoli
Subjects: Optimization and Control
AbstractAn 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.An exact algorithm for graph partitioning.
Thu, 12/10/2009 - 16:01 — SomNambulAuthors: William Hager, Dzung Phan, Hongchao Zhang
Subjects: Optimization and Control
AbstractAn exact algorithm is presented for solving edge weighted graph partitioning
problems. The algorithm is based on a branch and bound method applied to a
continuous quadratic programming formulation of the problem. Lower bounds are
obtained by decomposing the objective function into convex and concave parts
and replacing the concave part by an affine underestimate. It is shown that the
best affine underestimate can be expressed in terms of the center and the
radius of the smallest sphere containing the feasible set.Gradient-based methods for sparse recovery.
Thu, 12/10/2009 - 16:01 — SomNambulAuthors: William Hager, Dzung Phan, Hongchao Zhang
Subjects: Optimization and Control
AbstractThe convergence rate is analyzed for the SpaSRA algorithm (Sparse
Reconstruction by Separable Approximation) for minimizing a sum $f (\m{x}) +
\psi (\m{x})$ where $f$ is smooth and $\psi$ is convex, but possibly nonsmooth.
It is shown that if $f$ is convex, then the error in the objective function at
iteration $k$, for $k$ sufficiently large, is bounded by $a/(b+k)$ for suitable
choices of $a$ and $b$. Moreover, if the objective function is strongly convex,
then the convergence is $R$-linear.
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