Article

Computational Optimization and Applications

, Volume 34, Issue 2, pp 155-182

Interior-Point Algorithms, Penalty Methods and Equilibrium Problems

  • Hande Y. BensonAffiliated withDecision Sciences Department, LeBow College of Business, Drexel University Email author 
  • , Arun SenAffiliated withDepartment of Operations Research and Financial Engineering, Princeton University
  • , David F. ShannoAffiliated withRUTCOR - Rutgers Center of Operations Research, Rutgers University
  • , Robert J. VanderbeiAffiliated withDepartment of Operations Research and Financial Engineering, Princeton University

Rent the article at a discount

Rent now

* Final gross prices may vary according to local VAT.

Get Access

Abstract

In this paper we consider the question of solving equilibrium problems—formulated as complementarity problems and, more generally, mathematical programs with equilibrium constraints (MPECs)—as nonlinear programs, using an interior-point approach. These problems pose theoretical difficulties for nonlinear solvers, including interior-point methods. We examine the use of penalty methods to get around these difficulties and provide substantial numerical results. We go on to show that penalty methods can resolve some problems that interior-point algorithms encounter in general.

Keywords

interior-point methods nonlinear programming penalty methods equilibrium problems complementarity