CONVERGENCE ANALYSIS OF A SAA UNCONSTRAINED OPTIMIZATION METHOD FOR A STOCHASTIC LINEAR COMPLEMENTARITY PROBLEM OVER SYMMETRIC CONES
Stochastic symmetric cone complementarity problem is a new stochastic equilibrium model, which includes stochastic nonnegative orthant cone complementarity problems, stochastic second-order cone complementarity problems and stochastic semi-definite complementarity problems as its special cases. In this article, by the Fischer-Burmeister function, a sample average approximation unconstrained optimization method is proposed to solve a stochastic symmetric cone linear complementarity problem. The almost sure convergence results are established based on some basic properties of Euclidean Jordan algebra and the property associated with the deterministic complementarity problem.
stochastic symmetric cone linear complementarity problem, Fischer-Burmeister function, sample average approximation (SAA), Euclidean Jordan algebra.