Simple Bilevel Programming and Extensions Part-II: Algorithms

Abstract

This article continues our study on simple bilevel and simple MPEC problems. In this article we focus on developing algorithms. We show how using the idea of a gap function one can represent a simple MPEC as a simple bilevel problem with non-smooth data. This motivates us first to develop an algorithm for a simple bilevel problem with non-smooth data and modify the scheme for the same to develop an algorithm for the simple MPEC problem. We also discuss how the simple bilevel formulation of a simple MPEC can help us in formulating a stopping criteria for the simple MPEC problem