Globally and superlinearly convergent QP-free algorithm for nonlinear constrained optimization

Liqun Qi, Y. F. Yang

Research output: Journal article publicationJournal articleAcademic researchpeer-review

20 Citations (Scopus)

Abstract

A new, infeasible QP-free algorithm for nonlinear constrained optimization problems is proposed. The algorithm is based on a continuously differentiable exact penalty function and on active-set strategy. After a finite number of iterations, the algorithm requires only the solution of two linear systems at each iteration. We prove that the algorithm is globally convergent toward the KKT points and that, if the second-order sufficiency condition and the strict complementarity condition hold, then the rate of convergence is superlinear or even quadratic. Moreover, we incorporate two automatic adjustment rules for the choice of the penalty parameter and make use of an approximated direction as derivative of the merit function so that only first-order derivatives of the objective and constraint functions are used.
Original languageEnglish
Pages (from-to)297-323
Number of pages27
JournalJournal of Optimization Theory and Applications
Volume113
Issue number2
DOIs
Publication statusPublished - 1 May 2002

Keywords

  • active set strategies
  • constrained optimization
  • global convergence
  • QP-free method
  • superlinear convergence

ASJC Scopus subject areas

  • Control and Optimization
  • Management Science and Operations Research
  • Applied Mathematics

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