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Optimization Tools for Solving Equilibrium Problems with Nonsmooth Data

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Abstract

The paper deals with the gap function approach for equilibrium problems with locally Lipschitz data. The gap function inherits the locally Lipschitz continuity of the data. Hence, the connections between its generalized directional derivatives, monotonicity conditions on the equilibrium bifunction and descent properties, can be analyzed. In turn, this analysis leads to devise two descent methods. Finally, the results of preliminary numerical tests are reported.

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Acknowledgments

The authors are members of the Gruppo Nazionale per l’Analisi Matematica, la Probabilità e le loro Applicazioni (GNAMPA—National Group for Mathematical Analysis, Probability and their Applications) of the Istituto Nazionale di Alta Matematica (INdAM—National Institute of Higher Mathematics).

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Authors and Affiliations

  1. Dipartimento di Informatica, Università di Pisa, Largo B.Pontecorvo 3, 56127, Pisa, Italy

    Giancarlo Bigi, Massimo Pappalardo & Mauro Passacantando

Authors
  1. Giancarlo Bigi
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  2. Massimo Pappalardo
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  3. Mauro Passacantando
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Correspondence to Massimo Pappalardo.

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Communicated by Jean-Pierre Crouzeix.

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Bigi, G., Pappalardo, M. & Passacantando, M. Optimization Tools for Solving Equilibrium Problems with Nonsmooth Data. J Optim Theory Appl 171, 887–905 (2016). https://doi.org/10.1007/s10957-016-0974-2

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  • DOI: https://doi.org/10.1007/s10957-016-0974-2

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