In this paper, we consider a class of stochastic mathematical programs with equilibrium constraints (SMPECs) that has been discussed by Lin and Fukushima (2003). Based on a reformulation given therein, we propose a regularization method for solving the problems. We show that, under a weak condition, an accumulation point of the generated sequence is a feasible point of the original problem. We also show that such an accumulation point is S-stationary to the problem under additional assumptions.

In this paper, we consider a class of stochastic mathematical programs with equilibrium constraints (SMPECs) that has been discussed by Lin and Fukushima (2003). Based on a reformulation given therein, we propose a regularization method for solving the problems. We show that, under a weak condition, an accumulation point of the generated sequence is a feasible point of the original problem. We also show that such an accumulation point is S-stationary to the problem under additional assumptions....

We present an inexact interior point proximal method to solve linearly constrained convex problems. In fact, we derive a primal-dual algorithm to solve the KKT conditions of the optimization problem using a modified version of the rescaled proximal method. We also present a pure primal method. The proposed proximal method has as distinctive feature the possibility of allowing inexact inner steps even for Linear Programming. This is achieved by using an error criterion that bounds the subgradient...

Based on conjugate duality we construct several gap functions for general variational inequalities and equilibrium problems, in the formulation of which a so-called perturbation function is used. These functions are written with the help of the Fenchel-Moreau conjugate of the functions involved. In case we are working in the convex setting and a regularity condition is fulfilled, these functions become gap functions. The techniques used are the ones considered in [Altangerel L., Boţ R.I., Wanka...