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Some optimization reformulations of the extended linear complementarity problem. (English) Zbl 1040.90550
Summary: We consider the extended linear complementarity problem (XLCP) introduced by O. L. Mangasarian and J.-S. Pang [SIAM J. Matrix Anal. Appl. 16, 359–368 (1995; Zbl 0835.90103)], of which the horizontal and vertical linear complementarity problems are two special cases. We give some new sufficient conditions for every stationary point of the natural bilinear program associated with XLCP to be a solution of XLCP. We further propose some unconstrianed and bound constrained reformulations for XLCP, and study the properties of their stationary points under assumptions similar to those for the bilinear program.

MSC:
90C33 Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming)
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