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