Existence of equilibria via Ekeland's principle

By Monica Bianchi, Gábor Kassay, Rita Pini. 2005

121 citations recorded by the source corpus.

Abstract In the literature, when dealing with equilibrium problems and the existence of their solutions, the most used assumptions are the convexity of the domain and the generalized convexity and monotonicity, together with some weak continuity assumptions, of the function. In this paper, we focus on conditions that do not involve any convexity concept, neither for the domain nor for the function involved. Starting from the well-known Ekeland's theorem for minimization problems, we find a suitable set of conditions on the function f that lead to an Ekeland's variational principle for equilibrium problems. Via the existence of e-solutions, we are able to show existence of equilibria on general closed sets for equilibrium problems and systems of equilibrium problems.

Subfields: Computational Theory and Mathematics, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/232b25308ef888fdd4e701c547b0d486a0cd91c0

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Theory and Mathematics

In Numerical Analysis

Citations in the corpus

An inexact subgradient algorithm for Equilibrium Problems (2011, background): “Assumption A4 can be recovered if we assume A2 and the following condition holds f (z, x) ≤ f (z, y) + f (y, x) ∀ x, y, z ∈ C, which is considered, for instance, in [3].”
Some generalizations of Ekeland-type variational principle with applications to equilibrium problems and fixed point theory (2008, background): “1 in [6] we can easily derive the existence results for a solution of EP when K is not necessarily compact.”
Ekeland's principle for vector equilibrium problems (2007, background): “1 in [4] (the scalar Ekeland’s principle) to the real function e∗( f ).”
Vectorial form of Ekeland-type variational principle with applications to vector equilibrium problems and fixed point theory (2007, background): “1 in [8] to the complete quasi-metric spaces and a W -distance setting.”