An SAA approach for solving a class of stochastic inverse optimal value problems

In this paper, we consider a class of stochastic inverse optimal value problems, in which the forward problem is a linear programming problem (LP), and the data in its constraints are affected by a random variable.The corresponding inverse optimal value problem can be reformulated as a mathematical program with stochastic linear complementarity constraints (MPSLCC).By employing the techniques of sample average approximation (SAA), we construct a series of smooth SAA subproblems and transform them into nonlinear programming problems by utilizing the smooth Fischer-Burmeister function for linear complementarity constraints.In addition, we prove that the sequence of global minimizer (KKT point) of these SAA subproblems converges with probability one (w.p.1) to a global minimizer (an S-stationary point) of MPSLCC under mild conditions.Finally, some numerical experiments are presented to show the availability of our method for solving the given stochastic inverse optimal value problems.