Revisiting the construction of gap functions for variational inequalities and equilibrium problems via conjugate duality

• Autorzy: Liana Cioban , Ernö Csetnek
• Języki publikacji: EN

Abstrakty

EN

Based on conjugate duality we construct several gap functions for general variational inequalities and equilibrium problems, in the formulation of which a so-called perturbation function is used. These functions are written with the help of the Fenchel-Moreau conjugate of the functions involved. In case we are working in the convex setting and a regularity condition is fulfilled, these functions become gap functions. The techniques used are the ones considered in [Altangerel L., Boţ R.I., Wanka G., On gap functions for equilibrium problems via Fenchel duality, Pac. J. Optim., 2006, 2(3), 667–678] and [Altangerel L., Boţ R.I., Wanka G., On the construction of gap functions for variational inequalities via conjugate duality, Asia-Pac. J. Oper. Res., 2007, 24(3), 353–371]. By particularizing the perturbation function we rediscover several gap functions from the literature. We also characterize the solutions of various variational inequalities and equilibrium problems by means of the properties of the convex subdifferential. In case no regularity condition is fulfilled, we deliver also necessary and sufficient sequential characterizations for these solutions. Several examples are illustrating the theoretical aspects.

Słowa kluczowe

EN

Variational inequalities; Gap functions; Dual gap functions; Equilibrium problems; Perturbation theory; Sequential optimality conditions

Kategorie tematyczne

• 90C33: Complementarity and equilibrium problems and variational inequalities (finite dimensions)
• 90C46: Optimality conditions, duality
• 58E35: Variational inequalities (global problems)
• 47A55: Perturbation theory
• 49N15: Duality theory
• 90C25: Convex programming

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2013
• Tom: 11
• Numer: 5
• Strony: 829-850

Daty

wydano

2013-05-01

online

2013-03-14

Twórcy

autor

Liana Cioban

• Babeş-Bolyai University

autor

Ernö Csetnek

• Chemnitz University of Technology

Bibliografia

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Identyfikatory

DOI

10.2478/s11533-012-0151-2