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Indexed by:期刊论文

Date of Publication:2018-07-01

Journal:JOURNAL OF INDUSTRIAL AND MANAGEMENT OPTIMIZATION

Included Journals:SCIE

Volume:14

Issue:3

Page Number:1143-1155

ISSN No.:1547-5816

Key Words:Nonsmooth optimization; proximal bundle method; subgradient; localization set; Chebychev center

Abstract:Motivated by the proximal-like bundle method [K. C. Kiwiel, Journal of Optimization Theory and Applications, 104(3) (2000), 589-603.], we establish a new proximal Chebychev center cutting plane algorithm for a type of nonsmooth optimization problems. At each step of the algorithm, a new optimality measure is investigated instead of the classical optimality measure. The convergence analysis shows that an epsilon-optimal solution can be obtained within O (1/epsilon(3)) iterations. The numerical result is presented to show the validity of the conclusion and it shows that the method is competitive to the classical proximal-like bundle method.