On the convergence of successive linear-quadratic programming algorithms

Richard H. Byrd*, Nicholas I.M. Gould, Jorge Nocedal, Richard A. Waltz

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

36 Scopus citations


The global convergence properties of a class of penalty methods for nonlinear programming are analyzed. These methods include successive linear programming approaches and, more specifically, the successive linear-quadratic programming approach presented by Byrd et al. [Math. Program., 100 (2004), pp. 27-48]. Every iteration requires the solution of two trust-region subproblems involving piecewise linear and quadratic models, respectively. It is shown that, for a fixed penalty parameter, the sequence of iterates approaches stationarity of the penalty function. A procedure for dynamically adjusting the penalty parameter is described, and global convergence results for it are established.

Original languageEnglish (US)
Pages (from-to)471-489
Number of pages19
JournalSIAM Journal on Optimization
Issue number2
StatePublished - 2006


  • Global convergence theory
  • Nonlinear optimization
  • Penalty parameter updates
  • Sequential linear programming

ASJC Scopus subject areas

  • Software
  • Theoretical Computer Science
  • Applied Mathematics


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