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On the numerical solution of Lasserre relaxations of unconstrained binary quadratic optimization problem
Soodeh Habibi, Michal Kocvara, Michael Stingl
The aim of this paper is to solve linear semidefinite programs arising from higher-order Lasserre relaxations of unconstrained binary quadratic optimization problems. For this we u…
Partial Gradient Optimal Thresholding Algorithms for a Class of Sparse Optimization Problems
Nan Meng, Yun-Bin Zhao, Michal Kocvara
The optimization problems with a sparsity constraint is a class of important global optimization problems. A typical type of thresholding algorithms for solving such a problem adop…
Barrier and penalty methods for low-rank semidefinite programming with application to truss topology design
Soodeh Habibi, Arefeh Kavand, Michal Kocvara +1
The aim of this paper is to solve large-and-sparse linear Semidefinite Programs (SDPs) with low-rank solutions. We propose to use a preconditioned conjugate gradient method within…
Newton-type Multilevel Optimization Method
Chin Pang Ho, Michal Kocvara, Panos Parpas
Inspired by multigrid methods for linear systems of equations, multilevel optimization methods have been proposed to solve structured optimization problems. Multilevel methods make…
A Subgradient Method for Free Material Design
Michal Kocvara, Yurii Nesterov, Yu Xia
A small improvement in the structure of the material could save the manufactory a lot of money. The free material design can be formulated as an optimization problem. However, due…
PENNON: Software for linear and nonlinear matrix inequalities
Michal Kocvara, Michael Stingl
The goal of this paper is to present an overview of the software collection for the solution of linear and nonlinear semidefinite optimization problems PENNON. In the first part we…