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 estimate 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.

Bigi, G., Passacantando, M. (2016). Gap functions for quasi-equilibria. JOURNAL OF GLOBAL OPTIMIZATION, 66(4), 791-810 [10.1007/s10898-016-0458-9].

Gap functions for quasi-equilibria

Passacantando, M
2016

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 estimate 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.
Articolo in rivista - Articolo scientifico
Descent algorithm; Error bound; Gap function; Quasi-equilibrium; Stationary point;
English
791
810
20
Bigi, G., Passacantando, M. (2016). Gap functions for quasi-equilibria. JOURNAL OF GLOBAL OPTIMIZATION, 66(4), 791-810 [10.1007/s10898-016-0458-9].
Bigi, G; Passacantando, M
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/392099
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