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An efficient algorithm for steepest descent method for unconstrained optimization

Mamat, Mustafa and Aw, Siew Yee and Mohd, Ismail (2009) An efficient algorithm for steepest descent method for unconstrained optimization. Journal of Science and Technology UTHM, 1 (1). pp. 13-25. ISSN 1985 – 8809

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Exact line searches along each steepest descent direction converge very slowly. Barzilai and Borwein suggested two stepsizes that ensures superlinear convergence and performs quite well. Barzilai-Borwein method is not monotone, thus it is not easy to be generalized for general nonlinear functions. A new stepsize enables fast convergence and possesses monotone property is proposed by Yuan. The new stepsize is modified to obtain modified new steepest descent method, which is for convex quadratic problems only is proposed by Yuan. The new steepest descent method uses the new stepsize after every m exact line search iterations. An algorithm for m=2 is proposed in this paper.

Item Type: Article
Uncontrolled Keywords: steepest descent; line search; unconstrained optimization; convergence; monotone
Subjects: Q Science > QA Mathematics
Depositing User: Nurhafiza Hamzah
Date Deposited: 20 Apr 2011 04:38
Last Modified: 29 Apr 2011 06:41
URI: http://eprints.uthm.edu.my/id/eprint/543
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