A nonmonotone PSB algorithm for solving unconstrained optimization

Authors:
Jiao Li;Yu-Fei Yang;Bo Yu
Affiliations:
College of Mathematics and Econometrics, Hunan University, Changsha, China 410082;College of Mathematics and Econometrics, Hunan University, Changsha, China 410082;College of Science, Hunan University of Technology, Zhuzhou, China 412008
Venue:
Computational Optimization and Applications
Year:
2012

Citing 9
Cited 0

A nonmonotone line search technique for Newton's method

SIAM Journal on Numerical Analysis
A truncated Newton method with nonmonotone line search for unconstrained optimization

Journal of Optimization Theory and Applications
On the Global Convergence of the BFGS Method for Nonconvex Unconstrained Optimization Problems

SIAM Journal on Optimization
Analysis of a Symmetric Rank-One Trust Region Method

SIAM Journal on Optimization
Convergence Properties of the BFGS Algoritm

SIAM Journal on Optimization
On the nonmonotone line search

Journal of Optimization Theory and Applications
Nonmonotone Globalization Techniques for the Barzilai-Borwein Gradient Method

Computational Optimization and Applications
Convergence of nonmonotone line search method

Journal of Computational and Applied Mathematics
Sufficient descent directions in unconstrained optimization

Computational Optimization and Applications

Quantified Score

Hi-index	0.00

Visualization

Abstract

PSB (Powell-Symmetric-Broyden) algorithm is a very important algorithm and has been extensively used in trust region methods. However, there are few studies on the line search type PSB algorithm. The primary reason is that the direction generated by this class of algorithms is not necessarily a descent direction of the objective function. In this paper, by combining a nonmonotone line search technique with the PSB method, we propose a nonmonotone PSB algorithm for solving unconstrained optimization. Under proper conditions, we establish global convergence and superlinear convergence of the proposed algorithm. At the same time we verify the efficiency of the proposed algorithm by some numerical experiments.