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.
Reviewer: Do Van Luu (Hanoi)


49J40 Variational inequalities
90C25 Convex programming
Full Text: DOI


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