Combined Monte Carlo sampling and penalty method for Stochastic nonlinear complementarity problems

Combined Monte Carlo sampling and penalty method for Stochastic nonlinear complementarity problems

In this paper, we consider a new formulation with recourse for a class of stochastic nonlinear complementarity problems. We show that the new formulation is equivalent to a smooth semi-infinite program that no longer contains recourse variables. We then propose a combined Monte Carlo sampling and penalty method for solving the problem in which the underlying sample space is assumed to be compac...

Monte Carlo Sampling and Penalty Method for Stochastic Mathematical Programs with Complementarity Constraints and Recourse∗

In this paper, we consider a new formulation for stochastic mathematical programs with complementarity constraints and recourse. We show that the new formulation is equivalent to a smooth semi-infinite program. Then, we propose a Monte Carlo sampling and penalty method for solving the problem. Comprehensive convergence analysis and numerical examples are included as well.

Optimality Conditions and Combined Monte Carlo Sampling and Penalty Method for Stochastic Mathematical Programs with Complementarity Constraints and Recourse∗

In this paper, we consider a new formulation for stochastic mathematical programs with complementarity constraints and recourse. We show that the new formulation is equivalent to a smooth semi-infinite program that does no longer contain recourse variables. Optimality conditions for the problem are deduced and connections among the conditions are investigated. Then, we propose a combined Monte ...

A box-constrained differentiable penalty method for nonlinear complementarity problems

New Reformulations and Smoothed Penalty Method for Stochastic Nonlinear Complementarity Problems

We consider the stochastic nonlinear complementarity problem (SNCP), which has been receiving much attention in the recent optimization world. We first formulate the problem as a stochastic mathematical program with equilibrium constraints (SMPEC) and then, in order to develop some efficient methods, we further give some reformulations of the SNCP. In particular, for the case where the random v...