New Quasi-Newton Equation and Related Methods for Unconstrained Optimization

J. Z. Zhang, N. Y. Deng and L. H. Chen

Journal of Optimization Theory and Applications, 1999, vol. 102, issue 1, No 10, 147-167

Abstract: Abstract In unconstrained optimization, the usual quasi-Newton equation is B k+1 s k=y k, where y k is the difference of the gradients at the last two iterates. In this paper, we propose a new quasi-Newton equation, $$B_{k + 1} s_k = \tilde y_k $$ , in which $$\tilde y_k $$ is based on both the function values and gradients at the last two iterates. The new equation is superior to the old equation in the sense that $$\tilde y_k $$ better approximates ∇ 2 f(x k+1)s k than y k. Modified quasi-Newton methods based on the new quasi-Newton equation are locally and superlinearly convergent. Extensive numerical experiments have been conducted which show that the new quasi-Newton methods are encouraging.

Keywords: Unconstrained optimization; quasi-Newton equations; quasi-Newton methods (search for similar items in EconPapers)
Date: 1999
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Citations: View citations in EconPapers (21)

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DOI: 10.1023/A:1021898630001

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