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An interior-point method for mpecs based on strictly feasible relaxations

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  • Miguel, Angel Víctor de
  • Friedlander, Michael P.
  • Nogales Martín, Francisco Javier
  • Scholtes, Stefan

Abstract

An interior-point method for solving mathematical programs with equilibrium constraints (MPECs) is proposed. At each iteration of the algorithm, a single primaldual step is computed from each subproblem of a sequence. Each subproblem is defined as a relaxation of the MPEC with a nonempty strictly feasible region. In contrast to previous approaches, the proposed relaxation scheme preserves the nonempty strict feasibility of each subproblem even in the limit. Local and superlinear convergence of the algorithm is proved even with a less restrictive strict complementarity condition than the standard one. Moreover, mechanisms for inducing global convergence in practice are proposed. Numerical results on the MacMPEC test problem set demonstrate the fast-local convergence properties of the algorithm.

Suggested Citation

  • Miguel, Angel Víctor de & Friedlander, Michael P. & Nogales Martín, Francisco Javier & Scholtes, Stefan, 2004. "An interior-point method for mpecs based on strictly feasible relaxations," DES - Working Papers. Statistics and Econometrics. WS ws042408, Universidad Carlos III de Madrid. Departamento de Estadística.
    • Handle: RePEc:cte:wsrepe:ws042408
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    1. X. M. Hu & D. Ralph, 2004. "Convergence of a Penalty Method for Mathematical Programming with Complementarity Constraints," Journal of Optimization Theory and Applications, Springer, vol. 123(2), pages 365-390, November.
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    Cited by:

    1. Gabriel, Steven A. & Leuthold, Florian U., 2010. "Solving discretely-constrained MPEC problems with applications in electric power markets," Energy Economics, Elsevier, vol. 32(1), pages 3-14, January.

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