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Global Convergence of a Smooth Approximation Method for Mathematical Programs with Complementarity Constraints

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  • Hongxia Yin
  • Jianzhong Zhang

Abstract

A new smoothing approach was given for solving the mathematical programs with complementarity constraints (MPCC) by using the aggregation technique. As the smoothing parameter tends to zero, if the KKT point sequence generated from the smoothed problems satisfies the second-order necessary condition, then any accumulation point of the sequence is a B-stationary point of MPCC if the linear independence constraint qualification (LICQ) and the upper level strict complementarity (ULSC) condition hold at the limit point. The ULSC condition is weaker than the lower level strict complementarity (LLSC) condition generally used in the literatures. Moreover, the method can be easily extended to the mathematical programs with general vertical complementarity constraints. Copyright Springer-Verlag 2006

Suggested Citation

  • Hongxia Yin & Jianzhong Zhang, 2006. "Global Convergence of a Smooth Approximation Method for Mathematical Programs with Complementarity Constraints," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 64(2), pages 255-269, October.
    • Handle: RePEc:spr:mathme:v:64:y:2006:i:2:p:255-269
    DOI: 10.1007/s00186-006-0076-2
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    References listed on IDEAS

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    1. Holger Scheel & Stefan Scholtes, 2000. "Mathematical Programs with Complementarity Constraints: Stationarity, Optimality, and Sensitivity," Mathematics of Operations Research, INFORMS, vol. 25(1), pages 1-22, February.
    2. J. J. Ye & X. Y. Ye, 1997. "Necessary Optimality Conditions for Optimization Problems with Variational Inequality Constraints," Mathematics of Operations Research, INFORMS, vol. 22(4), pages 977-997, November.
    3. Stefan Scholtes & Michael Stöhr, 2001. "How Stringent is the Linear Independence Assumption for Mathematical Programs with Complementarity Constraints?," Mathematics of Operations Research, INFORMS, vol. 26(4), pages 851-863, November.
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