Abstract and Applied Analysis

An Approximate Quasi-Newton Bundle-Type Method for Nonsmooth Optimization

Jie Shen, Li-Ping Pang, and Dan Li

Full-text: Open access

Abstract

An implementable algorithm for solving a nonsmooth convex optimization problem is proposed by combining Moreau-Yosida regularization and bundle and quasi-Newton ideas. In contrast with quasi-Newton bundle methods of Mifflin et al. (1998), we only assume that the values of the objective function and its subgradients are evaluated approximately, which makes the method easier to implement. Under some reasonable assumptions, the proposed method is shown to have a Q-superlinear rate of convergence.

Article information

Source
Abstr. Appl. Anal., Volume 2013, Special Issue (2012), Article ID 697474, 7 pages.

Dates
First available in Project Euclid: 26 February 2014

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1393450427

Digital Object Identifier
doi:10.1155/2013/697474

Mathematical Reviews number (MathSciNet)
MR3045068

Zentralblatt MATH identifier
1278.90315

Citation

Shen, Jie; Pang, Li-Ping; Li, Dan. An Approximate Quasi-Newton Bundle-Type Method for Nonsmooth Optimization. Abstr. Appl. Anal. 2013, Special Issue (2012), Article ID 697474, 7 pages. doi:10.1155/2013/697474. https://projecteuclid.org/euclid.aaa/1393450427


Export citation