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.
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References
J. B. Rosen, The Gradient Projection Method for Nonlinear Programming, Part: Linear Constraints,SIAM J. Appl. Math.,8 (1960), 181–217.
X.-S. Zhang, On the Convergence of Rosen's Gradient Projection Method: Three-Dimensional Case,Acta Mathematicae Applicatae Sinica (in Chinese),8 1 (1985), 125–128.
D.-Z. Du, Remarks on the Convergence of Rosen's Gradient Projection Method, MSRI Technique Report 01718-86.
He Guang-Zhong, Proof of Convergence of the Rosen's Gradient Projection Method,Journal of Chengdu University of Science and Technology (in Chinese),1 (1987), 55–68.
M. S. Bazarra and C. M. Shetty, Nonlinear Programming: Theory and Algorithm, John Wiley & Sons, 1979.
W. I. Zangwill, Nonlinear Programming: A Unitfied Approach, Prentice-Hall, 1969.
D.-Z. Du and X.-S. Zhang. A Convergence Theorem for Rosen's Gradient Projection Method. MSRI Technique Report 02518-86.
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He, G. Rosen's Gradient Projection with discrete steps. Acta Mathematicae Applicatae Sinica 6, 1–10 (1990). https://doi.org/10.1007/BF02014710
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DOI: https://doi.org/10.1007/BF02014710