A least-square semismooth Newton method for the second-order cone complementarity problem

Shaohua Pan, Jein Shan Chen

    Research output: Contribution to journalArticlepeer-review

    2 Citations (Scopus)

    Abstract

    We present a nonlinear least-square formulation for the second-order cone complementarity problem based on the Fischer-Burmeister (FB) function and the plus function. This formulation has two-fold advantages. First, the operator involved in the over-determined system of equations inherits the favourable properties of the FB function for local convergence, for example, the (strong) semi-smoothness; second, the natural merit function of the over-determined system of equations share all the nice features of the class of merit functions fYF studied in [J.-S. Chen and P. Tseng, An unconstrained smooth minimization reformulation of the second-order cone complementarity problem, Math. Program. 104 (2005), pp. 293-327] for global convergence. We propose a semi-smooth Levenberg-Marquardt method to solve the arising over-determined system of equations, and establish the global and local convergence results. Among others, the superlinear (quadratic) rate of convergence is obtained under strict complementarity of the solution and a local error bound assumption, respectively. Numerical results verify the advantages of the least-square reformulation for difficult problems.

    Original languageEnglish
    Pages (from-to)1-22
    Number of pages22
    JournalOptimization Methods and Software
    Volume26
    Issue number1
    DOIs
    Publication statusPublished - 2011 Feb

    Keywords

    • Fischer-Burmeister function
    • Levenberg-Marquardt method
    • second-order cone complementarity problem
    • semi-smooth

    ASJC Scopus subject areas

    • Software
    • Control and Optimization
    • Applied Mathematics

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