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

Let K n be the second-order cone in R n , where n ≥ ~3. Given a vector q ∈ R n and an n × n matrix G, the second order cone linear complementarity problem SOLCP(G, q) is to find a vector x ∈ R n such that x ∈ K n , y := G x + q ∈ K n and x T y = 0. The matrix G is said to have the Q-property if SOLCP(G, q) has a solution for all q ∈ R n . An n × n matrix G is called a cone automorphism if G K n = K n . 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). [ABSTRACT FROM AUTHOR]