In 1960, J. B. Rosen gave a famous Gradient Projection Method in [1]. But the convergenceof the algorithm has not been proved for a Jong time. Many authors paid much attention to thisproblem, such as X.S. Zhang proved...In 1960, J. B. Rosen gave a famous Gradient Projection Method in [1]. But the convergenceof the algorithm has not been proved for a Jong time. Many authors paid much attention to thisproblem, such as X.S. Zhang proved in [2] (1984) that the limit point of {x_k} which is generatedby Rosen's algorithm is a K-T piont for a 3-dimensional caes, if {x_k} is convergent. D. Z. Duproved in [3] (1986) that Rosen's algorithm is convergent for 4-dimensional.In [4] (1986), theauthor of this paper gave a general proof of the convergence of Rosen's Gradient Projection Methodfor an n-dimensional case. As Rosen's method requires exact line search, we know that exact linesearch is very difficult on computer.In this paper a line search method of discrete steps are presentedand the convergence of the algorithm is proved.展开更多
文摘In 1960, J. B. Rosen gave a famous Gradient Projection Method in [1]. But the convergenceof the algorithm has not been proved for a Jong time. Many authors paid much attention to thisproblem, such as X.S. Zhang proved in [2] (1984) that the limit point of {x_k} which is generatedby Rosen's algorithm is a K-T piont for a 3-dimensional caes, if {x_k} is convergent. D. Z. Duproved in [3] (1986) that Rosen's algorithm is convergent for 4-dimensional.In [4] (1986), theauthor of this paper gave a general proof of the convergence of Rosen's Gradient Projection Methodfor an n-dimensional case. As Rosen's method requires exact line search, we know that exact linesearch is very difficult on computer.In this paper a line search method of discrete steps are presentedand the convergence of the algorithm is proved.
