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Rosen's Gradient Projection with discrete steps

Rosen's Gradient Projection with discrete steps In 1960, J. B. Rosen gave a famous Gradient Projection Method in [1]. But the convergence of the algorithm has not been proved for a long time. Many authors paid much attention to this problem, such as X.S. Zhang proved in [2] (1984) that the limit point of {x k} which is generated by Rosen's algorithm is a K-T piont for a 3-dimensional caes, if {x k} is convergent. D. Z. Du proved in [3] (1986) that Rosen's algorithm is convergent for 4-dimensional. In [4] (1986), the author of this paper gave a general proof of the convergence of Rosen's Gradient Projection Method for ann-dimensional case. As Rosen's method requires exact line search, we know that exact line search is very difficult on computer. In this paper a line search method of discrete steps are presented and the convergence of the algorithm is proved. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Mathematicae Applicatae Sinica Springer Journals

Rosen's Gradient Projection with discrete steps

Acta Mathematicae Applicatae Sinica , Volume 6 (1) – Jul 15, 2005

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Publisher
Springer Journals
Copyright
Copyright © 1990 by Science Press, Beijing, China and Allerton Press, Inc., New York, U.S.A.
Subject
Mathematics; Applications of Mathematics; Math Applications in Computer Science; Theoretical, Mathematical and Computational Physics
ISSN
0168-9673
eISSN
1618-3932
DOI
10.1007/BF02014710
Publisher site
See Article on Publisher Site

Abstract

In 1960, J. B. Rosen gave a famous Gradient Projection Method in [1]. But the convergence of the algorithm has not been proved for a long time. Many authors paid much attention to this problem, such as X.S. Zhang proved in [2] (1984) that the limit point of {x k} which is generated by Rosen's algorithm is a K-T piont for a 3-dimensional caes, if {x k} is convergent. D. Z. Du proved in [3] (1986) that Rosen's algorithm is convergent for 4-dimensional. In [4] (1986), the author of this paper gave a general proof of the convergence of Rosen's Gradient Projection Method for ann-dimensional case. As Rosen's method requires exact line search, we know that exact line search is very difficult on computer. In this paper a line search method of discrete steps are presented and the convergence of the algorithm is proved.

Journal

Acta Mathematicae Applicatae SinicaSpringer Journals

Published: Jul 15, 2005

References