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Hybrid Approach with Active Set Identification for Mathematical Programs with Complementarity Constraints

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  • G. H. Lin

    (Dalian University of Technology)

  • M. Fukushima

    (Kyoto University)

Abstract

We consider a mathematical program with complementarity constraints (MPCC). Our purpose is to develop methods that enable us to compute a solution or a point with some kind of stationarity to MPCC by solving a finite number of nonlinear programs. We apply an active set identification technique to a smoothing continuation method (Ref. 1) and propose a hybrid algorithm for solving MPCC. We develop also two modifications: one makes use of an index addition strategy; the other adopts an index subtraction strategy. We show that, under reasonable assumptions, all the proposed algorithms possess a finite termination property. Further discussions and numerical experience are given as well

Suggested Citation

  • G. H. Lin & M. Fukushima, 2006. "Hybrid Approach with Active Set Identification for Mathematical Programs with Complementarity Constraints," Journal of Optimization Theory and Applications, Springer, vol. 128(1), pages 1-28, January.
    • Handle: RePEc:spr:joptap:v:128:y:2006:i:1:d:10.1007_s10957-005-7549-y
    DOI: 10.1007/s10957-005-7549-y
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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.
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    Cited by:

    1. Daniel Ralph & Oliver Stein, 2011. "The C-Index: A New Stability Concept for Quadratic Programs with Complementarity Constraints," Mathematics of Operations Research, INFORMS, vol. 36(3), pages 504-526, August.
    2. Suhong Jiang & Jin Zhang & Caihua Chen & Guihua Lin, 2018. "Smoothing partial exact penalty splitting method for mathematical programs with equilibrium constraints," Journal of Global Optimization, Springer, vol. 70(1), pages 223-236, January.
    3. Nguyen Huy Chieu & Gue Myung Lee, 2013. "A Relaxed Constant Positive Linear Dependence Constraint Qualification for Mathematical Programs with Equilibrium Constraints," Journal of Optimization Theory and Applications, Springer, vol. 158(1), pages 11-32, July.

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