Copositivity tests based on the linear complementarity problem

Carmo Brás (), Gabriele Eichfelder () and Joaquim Júdice ()

Computational Optimization and Applications, 2016, vol. 63, issue 2, 493 pages

Abstract: We present copositivity tests based on new necessary and sufficient conditions which require the solution of linear complementarity problems (LCP). We propose methodologies involving Lemke’s method, an enumerative algorithm and a linear mixed-integer programming formulation to solve the required LCPs. Moreover, we discuss a new necessary condition for (strict) copositivity based on solving a linear program, which can be used as a preprocessing step. The algorithms with these three different variants are thoroughly applied to test matrices from the literature and to max-clique instances with matrices of order up to $$496\times 496$$ 496 × 496 . We compare our procedures with three other copositivity tests from the literature as well as with a general global optimization solver. The numerical results are very promising and equally good and in many cases better than the results reported elsewhere. Copyright Springer Science+Business Media New York 2016

Keywords: Conic optimization; Copositivity; Complementarity problems; Linear programming; 15A48; 90C33; 65F30; 65K99; 90C26 (search for similar items in EconPapers)
Date: 2016
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Citations: View citations in EconPapers (3)

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DOI: 10.1007/s10589-015-9772-2

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