Sufficient descent directions in unconstrained optimization

Authors:
Xiao-Min An;Dong-Hui Li;Yunhai Xiao
Affiliations:
College of Mathematics and Econometrics, Hunan University, Changsha, Peoples Republic of China 410082;College of Mathematics and Econometrics, Hunan University, Changsha, Peoples Republic of China 410082;Institute of Applied Mathematics, College of Mathematics and Information Science, Henan University, Kaifeng, Peoples Republic of China 475000
Venue:
Computational Optimization and Applications
Year:
2011

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Abstract

Descent property is very important for an iterative method to be globally convergent. In this paper, we propose a way to construct sufficient descent directions for unconstrained optimization. We then apply the technique to derive a PSB (Powell-Symmetric-Broyden) based method. The PSB based method locally reduces to the standard PSB method with unit steplength. Under appropriate conditions, we show that the PSB based method with Armijo line search or Wolfe line search is globally and superlinearly convergent for uniformly convex problems. We also do some numerical experiments. The results show that the PSB based method is competitive with the standard BFGS method.