IJPAM: Volume 44, No. 3 (2008)

SOLVING NONSMOOTH CONVEX OPTIMIZATION WITH
A NONMONOTONE TRUST REGION ALGORITHM

Yan Zhao$^1$, Nengzhu Gu$^2$
$^{1,2}$School of Science
University of Shanghai for Science and Technology
Shanghai, 200093, P.R. CHINA
$^1$e-mail: zhaoyanem@hotmail.com
$^2$e-mail: gnzemail@hotmail.com


Abstract.This paper concerns a nonmonotone trust region algorithm for nonsmooth convex optimization problems. The original nonsmooth function was converted into a continuously differentiable function via the Moreau-Yosida regularization, then used approximate values of the converted function and its gradient, the corresponding subproblem can be solved by a nonmonotone scheme. Under suitable assumptions, the algorithm is proved to be global and superlinear convergence.

Received: September 30, 2007

AMS Subject Classification: 90C30

Key Words and Phrases: convex optimization, Moreau-Yosida regulariztion, trust region method, convergence

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2008
Volume: 44
Issue: 3