Active-set projected trust-region algorithm for box-constrained nonsmooth equations

Liqun Qi, X. J. Tong, D. H. Li

Research output: Journal article publicationJournal articleAcademic researchpeer-review

51 Citations (Scopus)


In this paper, by means of an active-set strategy, we present a trust-region method for solving box-constrained nonsmooth equations. Nice properties of the proposed method include: (a) all iterates remain feasible; (b) the search direction, as adequate combination of the projected gradient direction and the trust-region direction, is an asymptotic Newton direction under mild conditions; (c) the subproblem of the proposed method, possessing the form of an unconstrained trust-region subproblem, can be solved by existing methods; (d) the subproblem of the proposed method is of reduced dimension, which is potentially cheaper when applied to solve large-scale problems. Under appropriate conditions, we establish global and local superlinear/quadratic convergence of the method. Preliminary numerical results are given.
Original languageEnglish
Pages (from-to)601-625
Number of pages25
JournalJournal of Optimization Theory and Applications
Issue number3
Publication statusPublished - 1 Mar 2004


  • Active-set strategy
  • Global convergence
  • Nonsmooth equations
  • Superlinear/quadratic convergence
  • Trust-region methods

ASJC Scopus subject areas

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


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