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X.-S. Zhang (1985)
On the Convergence of Rosen's Gradient Projection Method: Three-Dimensional CaseActa Mathematicae Applicatae Sinica, 8
J. Rosen (1960)
The Gradient Projection Method for Nonlinear Programming. Part I. Linear ConstraintsJournal of The Society for Industrial and Applied Mathematics, 8
J. B. Rosen (1960)
The Gradient Projection Method for Nonlinear Programming, Part: Linear ConstraintsSIAM J. Appl. Math., 8
He Guang-Zhong (1987)
Proof of Convergence of the Rosen's Gradient Projection MethodJournal of Chengdu University of Science and Technology, 1
D. Du (1987)
Remarks on the convergence of Rosen's gradient projection methodActa Mathematicae Applicatae Sinica, 3
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.
Acta Mathematicae Applicatae Sinica – Springer Journals
Published: Jul 15, 2005
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