Release Time:2019-03-12  Hits:

Indexed by: Journal Article

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: 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.