A Survey of Quasi-Newton Equations and Quasi-Newton Methods for Optimization

Chengxian Xu and Jianzhong Zhang ()

Annals of Operations Research, 2001, vol. 103, issue 1, 213-234

Abstract: Quasi-Newton equations play a central role in quasi-Newton methods for optimization and various quasi-Newton equations are available. This paper gives a survey on these quasi-Newton equations and studies properties of quasi-Newton methods with updates satisfying different quasi-Newton equations. These include single-step quasi-Newton equations that use only gradient information and that use both gradient and function value information in one step, and multi-step quasi-Newton equations that use the gradient information in last m steps. Main properties of quasi-Newton methods with updates satisfying different quasi-Newton equations are studied. These properties include the finite termination property, invariance, heredity of positive definite updates, consistency of search directions, global convergence and local superlinear convergence properties. Copyright Kluwer Academic Publishers 2001

Keywords: quasi-Newton equations; quasi-Newton methods; finite termination; positive definiteness; convergence properties (search for similar items in EconPapers)
Date: 2001
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DOI: 10.1023/A:1012959223138

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