Box-constrained minimization reformulations of complementarity problems in second-order cones

Authors:
R. Andreani;A. Friedlander;M. P. Mello;S. A. Santos
Affiliations:
Department of Applied Mathematics, IMECC-UNICAMP, University of Campinas, Campinas, Brazil 13081-970;Department of Applied Mathematics, IMECC-UNICAMP, University of Campinas, Campinas, Brazil 13081-970;Department of Applied Mathematics, IMECC-UNICAMP, University of Campinas, Campinas, Brazil 13081-970;Department of Applied Mathematics, IMECC-UNICAMP, University of Campinas, Campinas, Brazil 13081-970
Venue:
Journal of Global Optimization
Year:
2008

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Abstract

Reformulations of a generalization of a second-order cone complementarity problem (GSOCCP) as optimization problems are introduced, which preserve differentiability. Equivalence results are proved in the sense that the global minimizers of the reformulations with zero objective value are solutions to the GSOCCP and vice versa. Since the optimization problems involved include only simple constraints, a whole range of minimization algorithms may be used to solve the equivalent problems. Taking into account that optimization algorithms usually seek stationary points, a theoretical result is established that ensures equivalence between stationary points of the reformulation and solutions to the GSOCCP. Numerical experiments are presented that illustrate the advantages and disadvantages of the reformulations.