Asymptotic Analysis of Sample Average Approximation for Stochastic Optimization Problems with Joint Chance Constraints via CVaR/DC Approximations

Conditional Value at Risk (CVaR) has been recently used to approximate a chance constraint. In this paper, we study the convergence of stationary points when sample average approximation (SAA) method is applied to a CVaR approximated joint chance constrained stochastic minimization problem. Specifically, we prove, under some moderate conditions, that optimal solutions and stationary points … Read more

Stochastic Nash Equilibrium Problems: Sample Average Approximation and Applications

This paper presents a Nash equilibrium model where the underlying objective functions involve uncertainty and nonsmoothness. The well known sample average approximation method is applied to solve the problem and the first order equilibrium conditions are characterized in terms of Clarke generalized gradients. Under some moderate conditions, it is shown that with probability one, a … Read more

Stochastic Mathematical Programs with Equilibrium Constraints, Modeling and Sample Average Approximation

In this paper, we discuss the sample average approximation (SAA) method applied to a class of stochastic mathematical programs with variational (equilibrium) constraints. To this end, we briefly investigate piecewise structure and directional differentiability of both — the lower level equilibrium solution and objective integrant. We show almost sure convergence of optimal values, optimal solutions … Read more