Limited memory bundle method for large bound constrained nonsmooth optimization: convergence analysis

作     者：Karmitsa, Napsu Makela, Marko M. 

作者机构：Univ Turku Dept Math FI-20014 Turku Finland 

出 版 物：《OPTIMIZATION METHODS & SOFTWARE》 (最优化方法与软件)

年 卷 期：2010年第25卷第6期

页      面：895-916页

核心收录：

学科分类：12[管理学] 1201[管理学-管理科学与工程(可授管理学、工学学位)] 07[理学] 070105[理学-运筹学与控制论] 0835[工学-软件工程] 0701[理学-数学] 

主　　题：nondifferentiable programming large-scale optimization bundle methods limited memory methods box constraints global convergence 

摘      要：Practical optimization problems often involve nonsmooth functions of hundreds or thousands of variables. As a rule, the variables in such large problems are restricted to certain meaningful intervals. In the article [N. Karmitsa and M.M. Makela, Adaptive limited memory bundle method for bound constrained large-scale nonsmooth optimization, Optimization (to appear)], we described an efficient limited-memory bundle method for large-scale nonsmooth, possibly nonconvex, bound constrained optimization. Although this method works very well in numerical experiments, it suffers from one theoretical drawback, namely, that it is not necessarily globally convergent. In this article, a new variant of the method is proposed, and its global convergence for locally Lipschitz continuous functions is proved.