On solvability of the complex linear complementarity problem (Q761979)

Using a perturbation technique, conditions are given for solvability of the complex linear complementarity problem \(z\in S\), \(Mz+q\in S^*\), \(Re<z,Mz+q>=0\) where S is a pointed polyhedral cone in \({\mathbb{C}}^ n\) and \(S^*\) the polar cone of S. Results obtained include, for example, proofs of the existence of a solution when M is positive definite, S- copositive or regular. If feasibility is also assumed, then some of these conditions on M are weakened.