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 exploiting parametric definitions of different kinds of convexity and monotonicity. This analysis leads to extending some known results for variational inequalities and linear EPs to the general case together with new equivalences. Stationarity and convexity properties of gap functions are investigated as well in this framework. Moreover, both new results on the existence of a unique solution and new error bounds based on gap functions with good convexity properties are obtained under weak quasimonotonicity or weak concavity assumptions.

Bigi, G., Passacantando, M. (2017). Auxiliary problem principles for equilibria. OPTIMIZATION, 66(12), 1955-1972 [10.1080/02331934.2016.1227808].

Auxiliary problem principles for equilibria

Passacantando, M
2017

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 exploiting parametric definitions of different kinds of convexity and monotonicity. This analysis leads to extending some known results for variational inequalities and linear EPs to the general case together with new equivalences. Stationarity and convexity properties of gap functions are investigated as well in this framework. Moreover, both new results on the existence of a unique solution and new error bounds based on gap functions with good convexity properties are obtained under weak quasimonotonicity or weak concavity assumptions.
No
Articolo in rivista - Articolo scientifico
Scientifica
auxiliary problem; Equilibrium problem; error bound; gap function; Minty equilibrium problem;
English
1955
1972
18
Bigi, G., Passacantando, M. (2017). Auxiliary problem principles for equilibria. OPTIMIZATION, 66(12), 1955-1972 [10.1080/02331934.2016.1227808].
Bigi, G; Passacantando, M
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/10281/392097
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