LAUSR

In the setting of a Euclidean Jordan algebra V with symmetric cone $$V_+$$V+, corresponding to a linear transformation M, a ‘weight vector’ $$w\in V_+$$w∈V+, and a $$q\in V$$q∈V, we consider the weighted linear complementarity problem wLCP(M, w, q) and (when w is in the interior of $$V_+$$V+) the interior point system IPS(M, w, q). When M is copositive on $$V_+$$V+ and q satisfies an interiority condition, we show that both the problems have solutions. A simple consequence, stated in the setting of $$\mathbb {R}^{n}$$Rn 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 $$\mathbf{P}_*$$P∗-matrices and may lead to interior point methods for solving copositive LCPs.