Geodesic
An Existence Result for Equilibrium Problems with Some Surjectivity Consequences
Journal of convex analysis, Tome 16 (2009) no. 3, pp. 807-826.

Voir la notice de l'article provenant de la source Heldermann Verlag

We present conditions for existence of solutions of equilibrium problems, which are sufficient in finite dimensional spaces, without making any monotonicity assumption on the bifunction which defines the problem. As a consequence we establish surjectivity of set-valued operators of the form T + λI, with λ > 0, where T satisfies a property weaker than monotonicity, which we call pre-monotonicity. We study next the notion of maximal pre-monotonicity. Finally we adapt our condition for non-convex optimization problems, obtaining as a by-product an alternative proof of Frank-Wolfe's Theorem.
Classification : 90C47, 49J35
Mots-clés : Equilibrium problems, convex feasibility problems, variational inequalities, convex optimization 
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     title = {An {Existence} {Result} for {Equilibrium} {Problems} with {Some} {Surjectivity} {Consequences}},
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A. N. Iusem; G. Kassay; W. Sosa. An Existence Result for Equilibrium Problems with Some Surjectivity Consequences. Journal of convex analysis, Tome 16 (2009) no. 3, pp. 807-826. http://geodesic.mathdoc.fr/item/JCA_2009_16_3_JCA_2009_16_3_a14/