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Semidefinite programming relaxations of non-convex problems in control and combinatorial optimization
Applications of semidefinite programming combinatorial optimization quadratic semi-definite programming bilinear matrix inequality
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2015/8/11
We point out some connections between applications of semidefinite programming in control and in combinatorial optimization. In both fields semidefinite programs arise as convex relaxations of NP-hard...
Semidefinite Programming Relaxations and Algebraic Optimization in Control
Control Algebraic Optimization
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2015/6/19
We present an overview of the essential elements of semidefinite programming as a computational tool for the analysis of systems and control problems. We make particular emphasis on general duality pr...
Linear Programming Relaxations of Quadratically Constrained Quadratic Programs
Quadratic Programming Semidefinite Programming relaxation Linear Programming
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2012/6/29
We investigate the use of linear programming tools for solving semidefinite programming relaxations of quadratically constrained quadratic problems. Classes of valid linear inequalities are presented,...
A Sequence of Relaxations Constraining Hidden Variable Models
Hidden Variable Models Relaxations
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2011/9/13
Many widely studied graphical models with latent variables lead to nontrivial constraints on the distribution of the observed variables.Inspired by the Bell inequalities in quantum mechanics, we refer...
Sherali-Adams Relaxations of Graph Isomorphism Polytopes
Sherali-Adams Relaxations Graph Isomorphism Polytopes Combinatorics
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2011/8/24
Abstract: We investigate the Sherali-Adams lift & project hierarchy applied to a graph isomorphism polytope whose integer points encode the isomorphisms between two graphs. In particular, the Sherali-...
Sparse PCA: Convex Relaxations, Algorithms and Applications
Sparse PCA Algorithms Applications
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2010/11/22
Given a sample covariance matrix, we examine the problem of maximizing the variance explained by a linear combination of the input variables while constraining the number of nonzero coefficients in th...