Characterization of Q-property for cone automorphisms in second-order cone linear complementarity problems

Let (Formula presented.) be the second-order cone in (Formula presented.), where n ≥ ~3. Given a vector (Formula presented.) and an n × n matrix G, the second order cone linear complementarity problem SOLCP(G, q) is to find a vector (Formula presented.) such that (Formula presented.) The matrix G is said to have the Q-property if SOLCP(G, q) has a solution for all (Formula presented.). An n × n matrix G is called a cone automorphism if (Formula presented.). In this paper, we obtain a simple characterization for the Q-property of a cone automorphism. This says that G has the Q-property if and only if zero is the only solution to SOLCP(G, 0).