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Solving non-monotone equilibrium problems via a DIRECT-type approach

Author

Listed:
  • Stefano Lucidi

    (Sapienza University of Rome)

  • Mauro Passacantando

    (University of Pisa)

  • Francesco Rinaldi

    (University of Padova)

Abstract

A global optimization approach for solving non-monotone equilibrium problems (EPs) is proposed. The class of (regularized) gap functions is used to reformulate any EP as a constrained global optimization program and some bounds on the Lipschitz constant of such functions are provided. The proposed global optimization approach is a combination of an improved version of the DIRECT algorithm, which exploits local bounds of the Lipschitz constant of the objective function, with local minimizations. Unlike most existing solution methods for EPs, no monotonicity-type condition is assumed in this paper. Preliminary numerical results on several classes of EPs show the effectiveness of the approach.

Suggested Citation

  • Stefano Lucidi & Mauro Passacantando & Francesco Rinaldi, 2022. "Solving non-monotone equilibrium problems via a DIRECT-type approach," Journal of Global Optimization, Springer, vol. 83(4), pages 699-725, August.
    • Handle: RePEc:spr:jglopt:v:83:y:2022:i:4:d:10.1007_s10898-021-01121-z
    DOI: 10.1007/s10898-021-01121-z
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    References listed on IDEAS

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