A simple version of bundle method with linear programming

作     者：Liu, Shuai 

作者机构：Univ Estadual Campinas IMECC Rua Sergio Buarque de Holanda 651 BR-13083859 Campinas SP Brazil 

出 版 物：《COMPUTATIONAL OPTIMIZATION AND APPLICATIONS》 (计算优化及其应用)

年 卷 期：2019年第72卷第2期

页      面：391-412页

核心收录：

学科分类：1201[管理学-管理科学与工程(可授管理学、工学学位)] 07[理学] 070104[理学-应用数学] 0701[理学-数学] 

基　　金：ARC [DP12100567] FAPESP [2017/15936-2] Fundacao de Amparo a Pesquisa do Estado de Sao Paulo (FAPESP) [17/15936-2] Funding Source: FAPESP 

主　　题：Bundle method Linear programming Trust region Nonsmooth optimization 

摘      要：Bundle methods have been well studied in nonsmooth optimization. In most of the bundle methods developed thus far (traditional bundle methods), at least one quadratic programming subproblem needs to be solved in each iteration. In this paper, a simple version of bundle method with linear programming is proposed. In each iteration, a cutting-plane model subject to a constraint constructed by an infinity norm is minimized. Without line search or trust region techniques, the convergence of the method can be shown. Additionally, the infinity norm in the constraint can be generalized to p-norm. Preliminary numerical experiments show the potential advantage of the proposed method for solving large scale problems.