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Exploiting symmetry in copositive programs via semidefinite hierarchies

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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. As a result we are able to compute new bounds for crossing number instances in complete bipartite graphs.

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Authors and Affiliations

  1. Biometris, Wageningen University and Research Center, Wageningen, The Netherlands

    Cristian Dobre

  2. Department of Econometrics and OR, Tilburg University, Tilburg, The Netherlands

    Juan Vera

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  1. Cristian Dobre
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  2. Juan Vera
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Correspondence to Juan Vera.

Additional information

Cristian Dobre: This work was initiated while affiliated with the Johann Bernoulli Institute of Mathematics and Computer Science, University of Groningen, The Netherlands. Supported from the Netherlands Organisation for Scientific Research (NWO) through grant no. 639.033.907.

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Dobre, C., Vera, J. Exploiting symmetry in copositive programs via semidefinite hierarchies. Math. Program. 151, 659–680 (2015). https://doi.org/10.1007/s10107-015-0879-0

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