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An, Xiao-Min; Li, Dong-Hui; Xiao, Yunhai

Sufficient descent directions in unconstrained optimization. (English) Zbl 1242.90223

Comput. Optim. Appl. 48, No. 3, 515-532 (2011).
Summary: 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.

Cited in 8 Documents

MSC:

90C30 Nonlinear programming

Keywords:

unconstrained optimization; sufficient descent direction; PSB method; global convergence; superlinear convergence
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\textit{X.-M. An} et al., Comput. Optim. Appl. 48, No. 3, 515--532 (2011; Zbl 1242.90223)
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