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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.

49J40Variational methods including variational inequalities
90C25Convex programming
Full Text: DOI
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