Studies On A Class Of (Stochastic) Mathematical Programs With Equilibrium Constraints

In this paper, we discuss a class of (stochastic) mathematical programs with equilib-rium constraints:1. Linear program with complementarity constraints(LPCC):when M-1is a M-matrix and dT M-1>0, we show that LPCC is equivalent to a linear program and make an extension of reference [2].2. Nonlinear program with complementarity constraints(NLPCC):First, under some conditions, we transform the NLPCC into a convex program; Then, we consider the ap-proximation problem by using the regularization problem of NLPCC and the convergence analysis is given.3. Stochastic linear program with complementarity constraints(SLPCC):First, un-der some conditions, we transform the SLPCC into a stochastic linear program. Then, we employ the sampling average approximation technique to approximate SLPCC and establish its convergence analysis. We finally report some preliminary numerical results.