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Gap functions for quasi-equilibria

Giancarlo Bigi(giancarlo.bigi***at***unipi.it)
Mauro Passacantando(mauro.passacantando***at***unipi.it)

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.

Keywords: quasi-equilibrium, gap function, stationary point, descent algorithm, error bound

Category 1: Complementarity and Variational Inequalities

Category 2: Other Topics (Game Theory )

Category 3: Convex and Nonsmooth Optimization (Nonsmooth Optimization )

Citation: Unpublished technical report, UniversitÓ di Pisa (soon online at http://eprints.adm.unipi.it/2355)

Download: [PDF]

Entry Submitted: 02/09/2016
Entry Accepted: 02/09/2016
Entry Last Modified: 02/09/2016

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