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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The work was supported by the NSF project of China granted 10771057 and the major project of Ministry of education of China granted 309023.
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An, XM., Li, DH. & Xiao, Y. Sufficient descent directions in unconstrained optimization. Comput Optim Appl 48, 515–532 (2011). https://doi.org/10.1007/s10589-009-9268-z
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DOI: https://doi.org/10.1007/s10589-009-9268-z