Adaptive barrier update strategies for nonlinear interior methods

Jorge Nocedal*, Andreas Wächter, Richard A. Waltz

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

78 Scopus citations


This paper considers strategies for selecting the barrier parameter at every iteration of an interior-point method for nonlinear programming. Numerical experiments suggest that heuristic adaptive choices, such as Mehrotra's probing procedure, outperform monotone strategies that hold the barrier parameter fixed until a barrier optimality test is satisfied. A new adaptive strategy is proposed based on the minimization of a quality function. The paper also proposes a globalization framework that ensures the convergence of adaptive interior methods, and examines convergence failures of the Mehrotra predictor-corrector algorithm. The barrier update strategies proposed in this paper are applicable to a wide class of interior methods and are tested in the two distinct algorithmic frameworks provided by the IPOPT and KNITRO software packages.

Original languageEnglish (US)
Pages (from-to)1674-1693
Number of pages20
JournalSIAM Journal on Optimization
Issue number4
StatePublished - 2008


  • Barrier methods
  • Constrained optimization
  • Interior-point methods
  • Nonlinear programming

ASJC Scopus subject areas

  • Software
  • Theoretical Computer Science
  • Applied Mathematics


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