A proximal bundle method with inexact data for convex nondifferentiable minimization

被引：14
|
作者：
Shen, Jie [1 ]
Xia, Zun-Quan
Pang, Li-Ping
机构：
[1] Dalian Univ Technol, Dept Appl Math, Dalian 116024, Peoples R China
[2] Liaoning Normal Univ, Sch Math, Dalian 116029, Peoples R China
[3] Dalian Univ Technol, Dept Phys, Dalian 116024, Peoples R China
来源：
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2007年 / 66卷 / 09期
基金：
中国国家自然科学基金;
关键词：
approximate subgradient; bundle method; convex optimization; nonlinear programming; nonsmooth optimization; proximal bundle method;
D O I：
10.1016/j.na.2006.02.039
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
A proximal bundle method with inexact data is presented for minimizing an unconstrained nonsmooth convex function f. At each iteration, only the approximate evaluations of f and its epsilon-subgradients are required and its search directions are determined via solving quadratic programmings. Compared with the pre-existing results, the polyhedral approximation model that we offer is more precise and a new term is added into the estimation term of the descent from the model. It is shown that every cluster of the sequence of iterates generated by the proposed algorithm is an exact solution of the unconstrained minimization problem. (c) 2007 Published by Elsevier Ltd.
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页码：2016 / 2027
页数：12
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