Simple Bilevel Programming and Extensions Part-II: Algorithms

TL;DR

This paper develops algorithms for simple bilevel and MPEC problems using gap functions, addressing non-smooth data and proposing stopping criteria, thus advancing solution methods for these classes of problems.

Contribution

It introduces a novel algorithmic framework for simple bilevel and MPEC problems based on gap functions and non-smooth data handling.

Findings

Algorithm for simple bilevel problems with non-smooth data

Modified scheme for simple MPEC problems

Proposed stopping criteria for simple MPECs

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