A bundle method for solving equilibrium problems

• 成果类型: Article; Proceedings Paper
• 署名作者: Nguyen, T. T. V.; Strodiot, J. J.; Nguyen, V. H.
• 署名单位: University of Namur; Vietnam National University Ho Chi Minh City (VNUHCM) System
• 刊物名称: MATHEMATICAL PROGRAMMING
• ISSN/ISSBN: 0025-5610
• DOI: 10.1007/s10107-007-0112-x
• 发表日期: 2009
• 页码: 529-552
• 关键词: variational-inequalities; CONVERGENCE; algorithms

摘要

We present a bundle method for solving nonsmooth convex equilibrium problems based on the auxiliary problem principle. First, we consider a general algorithm that we prove to be convergent. Then we explain how to make this algorithm implementable. The strategy is to approximate the nonsmooth convex functions by piecewise linear convex functions in such a way that the subproblems are easy to solve and the convergence is preserved. In particular, we introduce a stopping criterion which is satisfied after finitely many iterations and which gives rise to Delta-stationary points. Finally, we apply our implementable algorithm for solving the particular case of singlevalued and multivalued variational inequalities and we find again the results obtained recently by Salmon et al. [18].