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Smooth Transformation of the Generalized Minimax Problem

Author

Listed:
  • G. Di Pillo

    (Università di Roma “La Sapienza,”)

  • L. Grippo

    (Università di Roma “La Sapienza,”)

  • S. Lucidi

    (Università di Roma “La Sapienza,”)

Abstract

We consider the generalized minimax problem, that is, the problem of minimizing a function φ(x)=F(g 1(x),...,g m(x)), where F is a smooth function and each g i is the maximum of a finite number of smooth functions. We prove that, under suitable assumptions, it is possible to construct a continuously differentiable exact barrier function, whose minimizers yield the minimizers of the function φ. In this way, the nonsmooth original problem can be solved by usual minimization techniques for unconstrained differentiable functions.

Suggested Citation

  • G. Di Pillo & L. Grippo & S. Lucidi, 1997. "Smooth Transformation of the Generalized Minimax Problem," Journal of Optimization Theory and Applications, Springer, vol. 95(1), pages 1-24, October.
    • Handle: RePEc:spr:joptap:v:95:y:1997:i:1:d:10.1023_a:1022627226891
    DOI: 10.1023/A:1022627226891
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    References listed on IDEAS

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    1. Robert Mifflin, 1977. "An Algorithm for Constrained Optimization with Semismooth Functions," Mathematics of Operations Research, INFORMS, vol. 2(2), pages 191-207, May.
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    Cited by:

    1. Adam B. Levy, 2005. "Convergence of Successive Approximation Methods with Parameter Target Sets," Mathematics of Operations Research, INFORMS, vol. 30(3), pages 765-784, August.
    2. Manlio Gaudioso & Giovanni Giallombardo & Giovanna Miglionico, 2022. "Essentials of numerical nonsmooth optimization," Annals of Operations Research, Springer, vol. 314(1), pages 213-253, July.
    3. Manlio Gaudioso & Giovanni Giallombardo & Giovanna Miglionico, 2006. "An Incremental Method for Solving Convex Finite Min-Max Problems," Mathematics of Operations Research, INFORMS, vol. 31(1), pages 173-187, February.
    4. Manlio Gaudioso & Giovanni Giallombardo & Giovanna Miglionico, 2020. "Essentials of numerical nonsmooth optimization," 4OR, Springer, vol. 18(1), pages 1-47, March.

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