New Conjugacy Conditions and Related Nonlinear Conjugate Gradient Methods

New Conjugacy Conditions and Related Nonlinear Conjugate Gradient Methods Conjugate gradient methods are a class of important methods for unconstrained optimization, especially when the dimension is large. This paper proposes a new conjugacy condition, which considers an inexact line search scheme but reduces to the old one if the line search is exact. Based on the new conjugacy condition, two nonlinear conjugate gradient methods are constructed. Convergence analysis for the two methods is provided. Our numerical results show that one of the methods is very efficient for the given test problems. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Applied Mathematics and Optimization Springer Journals

New Conjugacy Conditions and Related Nonlinear Conjugate Gradient Methods

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Publisher
Springer Journals
Copyright
Copyright © Inc. by 2000 Springer-Verlag New York
Subject
Mathematics; Calculus of Variations and Optimal Control; Optimization; Systems Theory, Control; Theoretical, Mathematical and Computational Physics; Mathematical Methods in Physics; Numerical and Computational Physics, Simulation
ISSN
0095-4616
eISSN
1432-0606
D.O.I.
10.1007/s002450010019
Publisher site
See Article on Publisher Site

Abstract

Conjugate gradient methods are a class of important methods for unconstrained optimization, especially when the dimension is large. This paper proposes a new conjugacy condition, which considers an inexact line search scheme but reduces to the old one if the line search is exact. Based on the new conjugacy condition, two nonlinear conjugate gradient methods are constructed. Convergence analysis for the two methods is provided. Our numerical results show that one of the methods is very efficient for the given test problems.

Journal

Applied Mathematics and OptimizationSpringer Journals

Published: Jan 1, 2001

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