In this paper, we consider some well-known equilibrium problems and their duals in a topological Hausdorff vector space X for a bifunction F defined on K x K,where K is a convex subset of X. Some necessary conditions are investigated, proving different results depending on the behaviour of F on the diagonal set. The concept of proper quasimonotonicity for bifunctions is defined, and the relationship with generalized monotonicity is investigated. The main result proves that the condition of proper quasimonotonicity is sharp in order to solve the dual equilibrium problem on every convex set.
Bianchi, M., & Pini, R. (2001). A note on equilibrium problems with properly quasimonotone bifunctions. JOURNAL OF GLOBAL OPTIMIZATION, 20(1), 67-76 [10.1023/A:1011234525151].
Citazione: | Bianchi, M., & Pini, R. (2001). A note on equilibrium problems with properly quasimonotone bifunctions. JOURNAL OF GLOBAL OPTIMIZATION, 20(1), 67-76 [10.1023/A:1011234525151]. | |
Tipo: | Articolo in rivista - Articolo scientifico | |
Carattere della pubblicazione: | Scientifica | |
Titolo: | A note on equilibrium problems with properly quasimonotone bifunctions | |
Autori: | Bianchi, M; Pini, R | |
Autori: | ||
Data di pubblicazione: | mag-2001 | |
Lingua: | English | |
Rivista: | JOURNAL OF GLOBAL OPTIMIZATION | |
Digital Object Identifier (DOI): | http://dx.doi.org/10.1023/A:1011234525151 | |
Appare nelle tipologie: | 01 - Articolo su rivista |