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A close look at auxiliary problem principles for equilibria

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

Abstract: The auxiliary problem principle allows solving a given equilibrium problem (EP) through an equivalent auxiliary problem with better properties. The paper investigates two families of auxiliary EPs: the classical auxiliary problems, in which a regularizing term is added to the equilibrium bifunction, and the regularized Minty EPs. The conditions that ensure the equivalence of a given EP with each of these auxiliary problems are investigated. This analysis leads to extending some known results for variational inequalities and linear EPs to the general case; moreover, new results are obtained as well. In particular, both new results on the existence and uniqueness of solutions and new error bounds based on gap functions with good convexity properties are obtained under weak quasimonotonicity or weak concavity assumptions.

Keywords: Equilibrium problem; auxiliary problem; Minty equilibrium problem; existence of solutions; gap function; error bound.

Category 1: Complementarity and Variational Inequalities

Category 2: Other Topics (Game Theory )

Citation: Technical report 1 December 2014, Dipartimento di Informatica, Università di Pisa

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Entry Submitted: 12/02/2014
Entry Accepted: 12/02/2014
Entry Last Modified: 12/02/2014

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