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EXPLOITING SYMMETRY IN COPOSITIVE PROGRAMS VIA SEMIDEFINITE HIERARCHIES

Cristian Dobre (cristian.dobre***at***wur.nl)
Juan Vera (j.c.veralizcano***at***uvt.nl)

Abstract: Copositive programming is a relative young field which has evolved into a highly active research area in mathematical optimization. An important line of research is to use semidefinite programming to approximate conic programming over the copositive cone. Two major drawbacks of this approach are the rapid growth in size of the resulting semidefinite programs, and the lack of information about the quality of the semidefinite programming approximations. These drawbacks are an inevitable consequence of the intractability of the generic problems that such approaches attempt to solve. To address such drawbacks, we develop customized solution approaches for highly symmetric copositive programs, which arise naturally in several contexts. For instance, symmetry properties of combinatorial problems are typically inherited when they are addressed via copositive programming.

Keywords: copositive programming, crossing number, approximation hierarchies

Category 1: Linear, Cone and Semidefinite Programming

Category 2: Combinatorial Optimization

Citation:

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Entry Submitted: 12/23/2013
Entry Accepted: 12/23/2013
Entry Last Modified: 02/19/2015

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