## Journal of Applied Mathematics

### A Decomposition Algorithm for Convex Nondifferentiable Minimization with Errors

#### Abstract

A decomposition algorithm based on proximal bundle-type method with inexact data is presented for minimizing an unconstrained nonsmooth convex function $f$. At each iteration, only the approximate evaluation of $f$ and its approximate subgradients are required which make the algorithm easier to implement. 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. Numerical tests emphasize the theoretical findings.

#### Article information

Source
J. Appl. Math., Volume 2012 (2012), Article ID 215160, 15 pages.

Dates
First available in Project Euclid: 15 March 2012

https://projecteuclid.org/euclid.jam/1331817624

Digital Object Identifier
doi:10.1155/2012/215160

Mathematical Reviews number (MathSciNet)
MR2861933

Zentralblatt MATH identifier
1235.65066

#### Citation

Lu, Yuan; Pang, Li-Ping; Shen, Jie; Liang, Xi-Jun. A Decomposition Algorithm for Convex Nondifferentiable Minimization with Errors. J. Appl. Math. 2012 (2012), Article ID 215160, 15 pages. doi:10.1155/2012/215160. https://projecteuclid.org/euclid.jam/1331817624