A new unconstrained differentiable merit function for box constrained variational inequality problems and a damped Gauss-Newton method

Defeng Sun, R.S. Womersley

Research output: Journal article publicationJournal articleAcademic researchpeer-review

30 Citations (Scopus)

Abstract

In this paper we propose a new unconstrained differentiable merit function f for box constrained variational inequality problems VIP(l, u, F). We study various desirable properties of this new merit function f and propose a Gauss-Newton method in which each step requires only the solution of a system of linear equations. Global and superlinear convergence results for VIP(l, u, F) are obtained Key results are the boundedness of the level sets of the merit function for any uniform P-function and the superlinear convergence of the algorithm without a nondegeneracy assumption. Numerical experiments confirm the good theoretical properties of the method.
Original languageEnglish
Pages (from-to)388-413
Number of pages26
JournalSIAM Journal on Optimization
Volume9
Issue number2
DOIs
Publication statusPublished - 1 Jan 1999
Externally publishedYes

Keywords

  • Box constraints
  • Gauss-Newton method
  • Merit functions
  • Superlinear convergence
  • Variational inequality problems

ASJC Scopus subject areas

  • Software
  • Theoretical Computer Science

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