Elsevier

Applied Mathematical Modelling

Volume 47, July 2017, Pages 811-825
Applied Mathematical Modelling

Global convergence of BFGS and PRP methods under a modified weak Wolfe–Powell line search☆,☆☆

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Highlights

  • •

    A modified Wolfe–Powell line search is presented.

  • •

    The BFGS method for general function under the line search has global convergence.

  • •

    The PRP method for general function under the line search has global convergence.

Abstract

The BFGS method is one of the most effective quasi-Newton algorithms for optimization problems. However, its global convergence for general functions is still open. In this paper, under a new line search technique, this problem is solved, and it is shown that other methods in the Broyden class also possess this property. Moreover, the global convergence of the PRP method is established in the case of this new line search. Numerical results are reported to show that the new line search technique is competitive to that of the normal line search.

Keywords

BFGS method
PRP method
Unconstrained optimization
Line search
Global convergence

2010 MSC

90C26

Cited by (0)

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This work is supported by the Guangxi Science Fund for Distinguished Young Scholars (No. 2015GXNSFGA139001), China NSF (Grant No. 11261006 and 11161003).

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This article belongs to the Special Issue: ICCPE 2015.

© 2017 Elsevier Inc.