Copositivity tests based on the linear complementarity problem

8 years 17 days ago

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Copositivity tests are presented based on new necessary and suﬃcient conditions requiring the solution of linear complementarity problems (LCP). Methodologies involving Lemke’s method, an enumerative algorithm and a linear mixed-integer programming formulation are proposed to solve the required LCPs. A new necessary condition for (strict) copositivity based on solving a Linear Program (LP) is also discussed, 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 up to dimension 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. Key Words: conic optimization, copositivity, complementarity problems, linear programming Mathematics ...

Carmo P. Brás, Gabriele Eichfelder, Joaquim

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