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Burer's Key Assumption for Semidefinite and Doubly Nonnegative Relaxations

Florian Jarre (jarre***at***opt.uni-duesseldorf.de)

Abstract: Burer has shown that completely positive relaxations of nonconvex quadratic programs with nonnegative and binary variables are exact when the binary variables satisfy a so-called key assumption. Here we show that introducing binary variables to obtain an equivalent problem that satisfies the key assumption will not improve the semidefinite relaxation, and only marginally improve the doubly nonnegative relaxation.

Keywords: Doubly nonnegative relaxation, completely positive program, key assumption.

Category 1: Linear, Cone and Semidefinite Programming (Semi-definite Programming )

Category 2: Combinatorial Optimization (Approximation Algorithms )

Category 3: Nonlinear Optimization (Quadratic Programming )

Citation: Technical report, Mathematisches Institut, Heinrich-Heine-Universität Düsseldorf, http://www.opt.uni-duesseldorf.de/~jarre/papers/2744.pdf


Entry Submitted: 09/23/2010
Entry Accepted: 09/23/2010
Entry Last Modified: 12/09/2010

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