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

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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.

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Authors and Affiliations

  1. Department of Applied Mathematics, IMECC-UNICAMP, University of Campinas, Campinas, SP, Brazil

    R. Andreani (Graduate Student)

  2. Department of Applied Mathematics, IMECC-UNICAMP, University of Campinas, Campinas, SP, Brazil

    A. Friedlander (Associate Professor)

  3. Department of Applied Mathematics, IMECC-UNICAMP, University of Campinas, Campinas, SP, Brazil

    J. M. Martínez (Professor)

Authors
  1. R. Andreani
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  2. A. Friedlander
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  3. J. M. Martínez
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Andreani, R., Friedlander, A. & Martínez, J.M. Solution of Finite-Dimensional Variational Inequalities Using Smooth Optimization with Simple Bounds. Journal of Optimization Theory and Applications 94, 635–657 (1997). https://doi.org/10.1023/A:1022601017090

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  • DOI: https://doi.org/10.1023/A:1022601017090

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