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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Abstract
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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