Sufficient descent directions in unconstrained optimization

Sufficient descent directions in unconstrained optimization

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Article ID: iaor20114154
Volume: 48
Issue: 3
Start Page Number: 515
End Page Number: 532
Publication Date: Apr 2011
Journal: Computational Optimization and Applications
Authors: , ,
Keywords: iterative methods, line search, steepest descent, global convergence
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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