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An efficient conjugate direction method with orthogonalization for large-scale quadratic optimization problems

Edouard Boudinov (edouard.boudinov***at***nl.fortisbank.com)
Arkadiy Manevich (aman***at***atlantis.dp.ua )

Abstract: A new conjugate direction method is proposed, which is based on an orthogonalization procedure and does not make use of line searches for the conjugate vector set construction. This procedure prevents the set of conjugate vectors from degeneracy and eliminates high sensitivity to computation errors pertinent to methods of conjugate directions, resulting in an efficient algorithm for solving large-scale ill-conditioned minimization problems without preconditioning. The advantages of our algorithms are illustrated by results of the extensive numerical experiments with large-scale quadratic functions.

Keywords: optimization, unconstrained minimization, conjugate directions methods, large-scale problems, orthogonalization

Category 1: Nonlinear Optimization

Category 2: Nonlinear Optimization (Unconstrained Optimization )

Citation: Edouard R. Boudinov and Arkadiy I. Manevich, "An efficient conjugate direction method with orthogonalization for large-scale quadratic optimization problems", Optimization Methods and Software, published electronically March 17, 2006: DOI. 10.1080/10556780500532209.

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Entry Submitted: 11/23/2005
Entry Accepted: 11/23/2005
Entry Last Modified: 03/20/2006

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