Line search filter methods for nonlinear programming: Motivation and global convergence

Andreas Wächter*, Lorenz T. Biegler

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

259 Scopus citations


Line search methods are proposed for nonlinear programming using Fletcher and Leyffer's filter method [Math. Program., 91 (2002), pp. 239-269], which replaces the traditional merit function. Their global convergence properties are analyzed. The presented framework is applied to active set sequential quadratic programming (SQP) and barrier interior point algorithms. Under mild assumptions it is shown that every limit point of the sequence of iterates generated by the algorithm is feasible, and that there exists at least one limit point that is a stationary point for the problem under consideration. A new alternative filter approach employing the Lagrangian function instead of the objective function with identical global convergence properties is briefly discussed.

Original languageEnglish (US)
Pages (from-to)1-31
Number of pages31
JournalSIAM Journal on Optimization
Issue number1
StatePublished - 2006


  • Barrier method
  • Filter method
  • Global convergence
  • Interior point method
  • Line search
  • Nonconvex constrained optimization
  • Nonlinear programming
  • Sequential quadratic programming

ASJC Scopus subject areas

  • Software
  • Theoretical Computer Science


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