Interior-point algorithms, penalty methods and equilibrium problems

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

Research output: Contribution to journalArticle

43 Scopus citations

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.

Original languageEnglish (US)
Pages (from-to)155-182
Number of pages28
JournalComputational Optimization and Applications
Volume34
Issue number2
DOIs
StatePublished - Jun 2006

All Science Journal Classification (ASJC) codes

  • Control and Optimization
  • Computational Mathematics
  • Applied Mathematics

Keywords

  • Complementarity
  • Equilibrium problems
  • Interior-point methods
  • Nonlinear programming
  • Penalty methods

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