Interior-Point Algorithms, Penalty Methods and Equilibrium Problems

  • Hande Benson
  • Arun Sen
  • David F. Shanno
  • Robert J. Vanderbei
    • Categories Complementarity and Variational Inequalities, Constrained Nonlinear Optimization, Game Theory Tags , , , , Short URL: https://optimization-online.org/?p=9429

    In this paper we consider the question of solving equilibrium problems---formulated as complementarity problems and, more generally, mathematical programs with equilibrium constraints (MPEC's)---as nonlinear programs, using an interior-point approach. These problems pose theoretical difficulties for nonlinear solvers, including interior-point methods. We examine the use of penalty methods to get around these difficulties, present an example from game theory where this makes a difference in practice, and provide substantial numerical results. We go on to show that penalty methods can resolve some problems that interior-point algorithms encounter in general.

    Citation

    Technical Report ORFE-03-02, Department of Operations Research and Financial Engineering, Princeton University, Princeton NJ, 08544, October 2003.

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