ON M-STEP MEMORY GRADIENT METHOD WITH WOLFE’S LINE SEARCH ^{∗}

Zhen-Jun SHI

Institute of Operations Research, Qufu Normal University, Qufu, Shandong 273165, P.R.China and Department of Applied Mathematics, Dalian University of Technology, Dalian, Liaoning 116024, P.R. China Email: zjshi@qfnu.edu.cn

July 22, 2002

Abstract

The paper presents an m-step memory gradient method for unconstrained optimization problem, and proves its global convergence under Wolfe’s line searches. The Algorithm sufficiently uses its previous m-step iterative information at each iteration. The idea makes us construct quick convergent algorithm and avoid computation and storage of some matrices associated with quasi-Newton methods. So that it is suitable to design new algorithm for large scale optimization problems. The linear convergence rate is investigated when the objective function is uniformly convex. Numerical experiments show that the new algorithm is very effective in practice.

Key words: Unconstrained optimization, m-step memory gradient method, Wolfe’s line search, convergence, numerical experiment.

AMS subject classifications: 90C30, 65K05,49M

∗The work is supported by NSF of China (10171054)