On the convergence of a trust-region method for solving constrained nonlinear equations with degenerate solutions

X. J. Tong, Liqun Qi

Research output: Journal article publicationJournal articleAcademic researchpeer-review

38 Citations (Scopus)


This paper presents a trust-region method for solving the constrained nonlinear equation F(x) = 0, x ∈ Ω, where Ω ⊂ Rnis a nonempty and closed convex set, F is defined on the open set containing Ω and is continuously differentiable. The iterates generated by the method are feasible. The method is globally and quadratically convergent under local error bounded assumption on F. The results obtained are extensions of the work of Yamashita Fukushima (Ref. 1) and Fan Yuan (Ref. 2) for unconstrained nonlinear equations. Numerical results show that the new algorithm works quite well.
Original languageEnglish
Pages (from-to)187-211
Number of pages25
JournalJournal of Optimization Theory and Applications
Issue number1
Publication statusPublished - 1 Oct 2004


  • Constrained nonlinear equations
  • error bound
  • global convergence
  • superlinear/quadratic convergence
  • trust-region methods

ASJC Scopus subject areas

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

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