Some Optimization Reformulations of the Extended Linear Complementarity Problem

Authors:
Michael V. Solodov
Affiliations:
Instituto de Matemática Pura e Aplicada, Estrada Dona Castorina 110, Jardim Botânico, Rio de Janeiro, RJ 22460-320, Brazil. solodov@impa.br
Venue:
Computational Optimization and Applications - Special issue on computational optimization—a tribute to Olvi Mangasarian, part II
Year:
1999

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Abstract

We consider the extended linear complementarity problem (XLCP)introduced by Mangasarian and Pang [22], of whichthe horizontal and vertical linear complementarity problemsare two special cases.We give some new sufficient conditions for everystationary point of the natural bilinear programassociated with XLCP to be a solution of XLCP. We furtherpropose some unconstrained and bound constrained reformulationsfor XLCP, and study the properties of their stationary pointsunder assumptions similar to those for thebilinear program.