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Solution of Finite-Dimensional Variational Inequalities Using Smooth Optimization with Simple Bounds

Author

Listed:
  • R. Andreani

    (University of Campinas)

  • A. Friedlander

    (University of Campinas)

  • J. M. Martínez

    (University of Campinas)

Abstract

The variational inequality problem is reduced to an optimization problem with a differentiable objective function and simple bounds. Theoretical results are proved, relating stationary points of the minimization problem to solutions of the variational inequality problem. Perturbations of the original problem are studied and an algorithm that uses the smooth minimization approach for solving monotone problems is defined.

Suggested Citation

  • R. Andreani & A. Friedlander & J. M. Martínez, 1997. "Solution of Finite-Dimensional Variational Inequalities Using Smooth Optimization with Simple Bounds," Journal of Optimization Theory and Applications, Springer, vol. 94(3), pages 635-657, September.
    • Handle: RePEc:spr:joptap:v:94:y:1997:i:3:d:10.1023_a:1022601017090
    DOI: 10.1023/A:1022601017090
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    References listed on IDEAS

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    1. J. Frédéric Bonnans & Clovis C. Gonzaga, 1996. "Convergence of Interior Point Algorithms for the Monotone Linear Complementarity Problem," Mathematics of Operations Research, INFORMS, vol. 21(1), pages 1-25, February.
    2. M. Seetharama Gowda & Jong-Shi Pang, 1992. "On Solution Stability of the Linear Complementarity Problem," Mathematics of Operations Research, INFORMS, vol. 17(1), pages 77-83, February.
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