A continuation method for the linear second-order cone complementarity problem

Abstract

We reformulate the linear second-order cone complementarity problem into a system of nonlinear equations. Our reformulation is different from others. Our algorithm for the reformulation can start from an arbitrary point. We prove that our algorithm approximates an optimum of the linear second-order cone complementarity problem in finite steps under certain conditions. Finally, we show that the system of nonlinear equations of our reformulation is nonsingular at optimum under certain conditions. © Springer-Verlag Berlin Heidelberg 2005.