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Weighted LCPs and interior point systems for copositive linear transformations on Euclidean Jordan algebras

M. S. Gowda(gowda***at***umbc.edu)

Abstract: In the setting of a Euclidean Jordan algebra V with symmetric cone V_+, corresponding to a linear transformation M, a `weight vector' w in V_+, and a q in V, we consider the weighted linear complementarity problem wLCP(M,w,q) and (when w is in the interior of V_+) the interior point system IPS(M,w,q). When M is copositive and q satisfies an interiority condition, we show that both the problems have solutions. A simple consequence, stated in the setting of R^n is that when M is a copositive plus matrix and q is strictly feasible for the linear complementarity problem LCP(M,q), the corresponding interior point system has a solution. This is analogous to a well-known result of Kojima et al. on P_*-matrices and may lead to interior point methods for solving copositive LCPs.

Keywords: Weighted LCP, Interior point system, Euclidean Jordan algebra, Degree, Copositive linear transformation

Category 1: Complementarity and Variational Inequalities

Citation: Research Report, Department of Mathematics and Statistics, University of Maryland Baltimore County, Baltimore, Maryland 21250, USA, July 2018.

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Entry Submitted: 07/25/2018
Entry Accepted: 07/25/2018
Entry Last Modified: 07/25/2018

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