Preprint A591/2008
An existence result for equilibrium problems with some surjectivity consequences

Wilfredo Sosa | Iusem, Alfredo N. | Kassay, Gabor

**Keywords: **
Equilibirum problems | Minty's theorem

We present conditions for existence of equilibrium problems, which are sufficient in the finite dimensional case, without
making any monotonicity assumptions on the underlying bifunction.
As a consequence we prove surjectivity of set-valued operators of the form T + aI, with a > 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 conditions for non-convex optimization problems, obtaining as a by-prodcut a new proof of Frank-Wolfe's Theorem.