Computational Optimization and Applications

, Volume 34, Issue 2, pp 155–182

Interior-Point Algorithms, Penalty Methods and Equilibrium Problems

  • Hande Y. Benson
  • Arun Sen
  • David F. Shanno
  • Robert J. Vanderbei
Article

DOI: 10.1007/s10589-005-3908-8

Cite this article as:
Benson, H.Y., Sen, A., Shanno, D.F. et al. Comput Optim Applic (2006) 34: 155. doi:10.1007/s10589-005-3908-8

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 methodsnonlinear programmingpenalty methodsequilibrium problemscomplementarity

Copyright information

© Springer Science + Business Media, Inc. 2006

Authors and Affiliations

  • Hande Y. Benson
    • 1
  • Arun Sen
    • 2
  • David F. Shanno
    • 3
  • Robert J. Vanderbei
    • 2
  1. 1.Decision Sciences DepartmentLeBow College of Business, Drexel UniversityPhiladelphia
  2. 2.Department of Operations Research and Financial EngineeringPrinceton UniversityPrinceton
  3. 3.RUTCOR - Rutgers Center of Operations ResearchRutgers UniversityNew Brunswick