Interior methods for mathematical programs with complementarity constraints

Sven Leyffer*, Gabriel López-Calva, Jorge Nocedal

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

127 Scopus citations


This paper studies theoretical and practical properties of interior-penalty methods for mathematical programs with complementarity constraints. A framework for implementing these methods is presented, and the need for adaptive penalty update strategies is motivated with examples. The algorithm is shown to be globally convergent to strongly stationary points, under standard assumptions. These results are then extended to an interior-relaxation approach. Superlinear convergence to strongly stationary points is also established. Two strategies for updating the penalty parameter are proposed, and their efficiency and robustness are studied on an extensive collection of test problems.

Original languageEnglish (US)
Pages (from-to)52-77
Number of pages26
JournalSIAM Journal on Optimization
Issue number1
StatePublished - 2007


  • Complementarity constraints
  • Equilibrium constraints
  • Exact penalty
  • Interior-point methods
  • Mathematical programs with complementarity constraints
  • Nonlinear programming

ASJC Scopus subject areas

  • Software
  • Theoretical Computer Science


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