Preprint A527/2007
A proximal point method for equilibrium problems in Hilbert spaces

Wilfredo Sosa Sandoval | Iusem, Alfredo

**Keywords: **
Proximal point | equilibrium problem | Maximal monotone operators | variational inequalities

We propose and analize a proximal point method for equilibrium problems in Hilbert spaces, which extends the well known proximal point method for variational inequalities. We prove global weak convergence of the generated sequence to a solution of the problem, assuming existence of solutions and rather weak monotonicity properties of the bifunction f which defines the equilibrium problem. We also present a reformulation of equilibrium problems as variational inequalities, under the same assumptions on f.