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Linear complementarity problems over symmetric cones: Characterization of Qb-transformations and existence results

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

Abstract: This paper is devoted to the study of the {symmetric cone linear complementarity problem} (SCLCP). In this context, our aim is to characterize the class Q_b in terms of larger classes, such as Q and R_0. For this, we introduce the class F and García's transformations. We studied them for concrete particular instances (such as second-order and semidefinite linear complementarity problems) and for specific examples (Lyapunov, Stein functions, among others). This naturally permits to establish noncoercive existence results for SCLCPs.

Keywords: Euclidean Jordan algebra, linear complementarity problem, symmetric cone, Q_b-transformation, Q-transformation, García’s transformation.

Category 1: Linear, Cone and Semidefinite Programming (Other )

Citation: Technical Report DIM-CMM Nº B-11/12-241, Diciembre/2011.

Download: [PDF]

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

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