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Global Convergence of a Modified Gradient Projection Method for Convex Constrained Problems

Global Convergence of a Modified Gradient Projection Method for Convex Constrained Problems In this paper, the continuously differentiable optimization problem min{f(x) : x ∈ Ω}, where Ω ∈ R n is a nonempty closed convex set, the gradient projection method by Calamai and More (Math. Programming, Vol.39. P.93-116, 1987) is modified by memory gradient to improve the convergence rate of the gradient projection method is considered. The convergence of the new method is analyzed without assuming that the iteration sequence {x k } of bounded. Moreover, it is shown that, when f(x) is pseudo-convex (quasi-convex) function, this new method has strong convergence results. The numerical results show that the method in this paper is more effective than the gradient projection method. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Mathematicae Applicatae Sinica Springer Journals

Global Convergence of a Modified Gradient Projection Method for Convex Constrained Problems

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Publisher
Springer Journals
Copyright
Copyright © 2006 by Springer-Verlag Berlin Heidelberg
Subject
Mathematics; Applications of Mathematics; Math Applications in Computer Science; Theoretical, Mathematical and Computational Physics
ISSN
0168-9673
eISSN
1618-3932
DOI
10.1007/s10255-006-0299-2
Publisher site
See Article on Publisher Site

Abstract

In this paper, the continuously differentiable optimization problem min{f(x) : x ∈ Ω}, where Ω ∈ R n is a nonempty closed convex set, the gradient projection method by Calamai and More (Math. Programming, Vol.39. P.93-116, 1987) is modified by memory gradient to improve the convergence rate of the gradient projection method is considered. The convergence of the new method is analyzed without assuming that the iteration sequence {x k } of bounded. Moreover, it is shown that, when f(x) is pseudo-convex (quasi-convex) function, this new method has strong convergence results. The numerical results show that the method in this paper is more effective than the gradient projection method.

Journal

Acta Mathematicae Applicatae SinicaSpringer Journals

Published: Jan 1, 2006

References