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A bundle method for solving equilibrium problems. (English) Zbl 1155.49006
Basing on the auxiliary problem principle, the authors study a boundle method for solving the nonsmooth convex equilibrium problem: finding $x^* \in C$ such that $f(x^*,y) \geq 0 \,\,{\text{for all}}\,\, y \in C$, and prove the convergence theorems for the general algorithm. Using a bundle strategy an implementable version of this algorithm is proposed together with the convergence results for the bundle algorithm. Some applications to variational inequality problems are also given.

MSC:
 49J40 Variational methods including variational inequalities 90C25 Convex programming
Full Text:
References:
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