The convergence of a Levenberg-Marquardt method for nonlinear inequalities

Hongxia Yin, Zheng Hai Huang, Liqun Qi

Research output: Journal article publicationJournal articleAcademic researchpeer-review

16 Citations (Scopus)


In this paper, we consider the least l2-norm solution for a possibly inconsistent system of nonlinear inequalities. The objective function of the problem is only first-order continuously differentiable. By introducing a new smoothing function, the problem is approximated by a family of parameterized optimization problems with twice continuously differentiable objective functions. Then a Levenberg-Marquardt algorithm is proposed to solve the parameterized smooth optimization problems. It is proved that the algorithm either terminates finitely at a solution of the original inequality problem or generates an infinite sequence. In the latter case, the infinite sequence converges to a least l2-norm solution of the inequality problem. The local quadratic convergence of the algorithm was produced under some conditions.
Original languageEnglish
Pages (from-to)687-716
Number of pages30
JournalNumerical Functional Analysis and Optimization
Issue number5-6
Publication statusPublished - 1 May 2008


  • Global convergence
  • Inconsistent
  • Least l -norm solution 2
  • Levenberg-Marquardt method
  • Local quadratic convergence
  • Nonlinear inequalities

ASJC Scopus subject areas

  • Applied Mathematics
  • Control and Optimization


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