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A close look at auxiliary problem principles for equilibria

Bigi, Giancarlo and Passacantando, Mauro (2014) A close look at auxiliary problem principles for equilibria. Technical Report del Dipartimento di Informatica . Università di Pisa, Pisa, IT. (Submitted)

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    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.

    Item Type: Book
    Uncontrolled Keywords: equilibrium problem; auxiliary problem; Minty equilibrium problem; existence of solutions; gap function; error bound.
    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: 09 Dec 2014 10:43
    Last Modified: 22 Dec 2014 14:21
    URI: http://eprints.adm.unipi.it/id/eprint/2316

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