Rosen's Gradient Projection with discrete steps
Tóm tắt
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.
Tài liệu tham khảo
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.