Unconstrained optimization reformulation of the generalized nonlinear complementarity problem and related method

Yi Ju Wang, Xin Zhen Zhang, Liqun Qi

Research output: Journal article publicationJournal articleAcademic researchpeer-review

7 Citations (Scopus)

Abstract

In this article, we first propose an unconstrained optimization reformulation of the generalized nonlinear complementarity problem (GNCP) over a polyhedral cone, and then discuss the conditions under which its any stationary point is a solution of the GNCP. The conditions which guarantee the nonsingularity and positive definiteness of the Hessian matrix of the objective function are also given. In the end, we design a Newton-type method to solve the GNCP and show the global and local quadratic convergence of the proposed method under certain assumptions.
Original languageEnglish
Pages (from-to)563-577
Number of pages15
JournalOptimization
Volume54
Issue number6
DOIs
Publication statusPublished - 1 Dec 2005

Keywords

  • GNCP
  • Optimization reformulation
  • Quadratical convergence

ASJC Scopus subject areas

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

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