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.