Taiwanese Journal of Mathematics

A MONOTONE GRADIENT METHOD VIA WEAK SECANT EQUATION FOR UNCONSTRAINED OPTIMIZATION

Wah June Leong, Malik Abu Hassan, and Mahboubeh Farid

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Abstract

In this paper we present a new algorithm of steepest descent type. A new technique for steplength computation and a monotone strategy are provided in the framework of the Barzilai and Borwein method. In contrast with Barzilai and Borwein approach's in which the steplength is computed by means of a simple approximation of the Hessian in the form of scalar multiple of identity and an interpretation of the secant equation, the new proposed algorithm considers another approximation of the Hessian based on the weak secant equation. By incorporating a simple monotone strategy, the resulting algorithm belongs to the class of monotone gradient methods with linearly convergence. Numerical results suggest that for non-quadratic minimization problem, the new method clearly outperforms the Barzilai-Borwein method.

Article information

Source
Taiwanese J. Math., Volume 14, Number 2 (2010), 413-423.

Dates
First available in Project Euclid: 18 July 2017

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1500405798

Digital Object Identifier
doi:10.11650/twjm/1500405798

Mathematical Reviews number (MathSciNet)
MR2655778

Zentralblatt MATH identifier
1203.90148

Subjects
Primary: 90C30: Nonlinear programming 65K05: Mathematical programming methods [See also 90Cxx]

Keywords
unconstrained optimization monotone gradient methods weak secant equation Barzilai-Borwein method

Citation

Leong, Wah June; Hassan, Malik Abu; Farid, Mahboubeh. A MONOTONE GRADIENT METHOD VIA WEAK SECANT EQUATION FOR UNCONSTRAINED OPTIMIZATION. Taiwanese J. Math. 14 (2010), no. 2, 413--423. doi:10.11650/twjm/1500405798. https://projecteuclid.org/euclid.twjm/1500405798


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