Sufficient descent directions in unconstrained optimization |
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Authors: | Xiao-Min An Dong-Hui Li Yunhai Xiao |
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Institution: | (1) College of Mathematics and Econometrics, Hunan University, Changsha, 410082, Peoples Republic of China;(2) Institute of Applied Mathematics, College of Mathematics and Information Science, Henan University, Kaifeng, 475000, Peoples Republic of China |
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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. |
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