Memory gradient method with Goldstein line search

Authors:
Zhen-Jun Shi;Jie Shen
Affiliations:
College of Operations Research and Management, Qufu Normal University, Rizhao, Shandong 276826, PR China and Department of Computer and Information Science, University of Michigan-Dearborn, Michig ...;Department of Computer and Information Science, University of Michigan-Dearborn, Michigan, MI48128-1491, USA
Venue:
Computers & Mathematics with Applications
Year:
2007

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Abstract

In this paper, we present a multi-step memory gradient method with Goldstein line search for unconstrained optimization problems and prove its global convergence under some mild conditions. We also prove the linear convergence rate of the new method when the objective function is uniformly convex. Numerical results show that the new algorithm is suitable to solve large-scale optimization problems and is more stable than other similar methods in practical computation.