Properties of expected residual functions arising from stochastic complementarity problems

Abstract

The stochastic nonlinear complementarity problem has been recently reformulated as an expected residual minimization (ERM) problem which minimizes an expected residual function defined by an NCP function. In this paper we study the properties of the expected residual functions defined by the min function and the Fischer-Burmeister function. In particular, the differentiability property of the expected residual functions is studied. In addition, we give a sufficient condition for the existence of a solution to the ERM problem.