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Gap functions for quasi-equilibria

Bigi, Giancarlo and Passacantando, Mauro Gap functions for quasi-equilibria. Technical Report del Dipartimento di Informatica, TR (16-01). Università di Pisa, Pisa, IT.

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    An approach for solving quasi-equilibrium problems (QEPs) is proposed relying on gap functions, which allow reformulating QEPs as global optimization problems. The (generalized) smoothness properties of a gap function are analysed and an upper estimates of its Clarke directional derivative is given. Monotonicity assumptions on both the equilibrium and constraining bifunctions are a key tool to guarantee that all the stationary points of a gap function actually solve QEP. A few classes of constraints satisfying such assumptions are identified covering a wide range of situations. Relying on these results, a descent method for solving QEP is devised and its convergence proved. Finally, error bounds are given in order to guarantee the boundedness of the sequence generated by the algorithm.

    Item Type: Book
    Subjects: Area01 - Scienze matematiche e informatiche > MAT/09 - Ricerca operativa
    Area13 - Scienze economiche e statistiche > SECS-S/06 - Metodi matematici dell'economia e delle scienze attuariali e finanziarie
    Divisions: Dipartimenti (from 2013) > DIPARTIMENTO DI INFORMATICA
    Depositing User: Giancarlo Bigi
    Date Deposited: 15 Feb 2016 12:01
    Last Modified: 15 Feb 2016 12:01
    URI: http://eprints.adm.unipi.it/id/eprint/2355

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