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Existence and stability results based on asymptotic analysis for semidefinite linear complementarity problems

Julio López(julio.lopez***at***usm.cl)
Rubén López(rlopez***at***ucsc.cl)
Hector Ramírez C.(hramirez***at***dim.uchile.cl)

Abstract: This work is devoted to the study of existence and stability results of semidefinite linear complementarity problems (SDLCP). Our approach consists of approximating the variational inequality formulation of the SDLCP by a sequence of suitable chosen variational inequalities. This provides particular estimates for the asymptotic cone of the solution set of the SDLCP. We thus obtain new coercive and noncoercive existence results, as well as new properties related to the continuity of the solution sets of the SDLCP (such as outer/upper semicontinuity, Lipschitz-type continuity, among others). Moreover, this asymptotic approach leads to a natural extension of the class of García linear transformations, formerly defined in the context of linear complementarity problems, to this SDLCP setting.

Keywords: Semide nite linear complementarity problems, asymptotic analysis, existence stability results.

Category 1: Linear, Cone and Semidefinite Programming (Semi-definite Programming )

Citation: Technical Report DIM-CMM Nº B-11/09-241, Septiembre/2011.

Download: [PDF]

Entry Submitted: 01/01/2012
Entry Accepted: 01/01/2012
Entry Last Modified: 01/01/2012

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