一种新的非线性共轭梯度方法及其收敛性(英文)

A NEW NONLINEAR CONJUGATE GRADIENT METHOD AND ITS GLOBAL CONVERGENCE

本文研究了一种新的求解无约束优化问题的非线性共轭梯度方法,其能够在广义Wolfe线搜索下保证充分下降条件:gT k dk≤(1-σ)||gk||2,并且具有全局收敛性,改进了传统CD方法(Fletcher,1987,[1])的缺陷.最后,通过与著名的CD方法(Fletcher,1987,[1])和PRP方法(Polak,Ribire,[2],Polak[3],1969)比较,结果显示新方法具有一定的研究意义.

In this paper, a new nonlinear conjugate gradient method is studied to solve the unconstrained optimization problems, which can guarantee the sufficient descent property： T gk^T dk 〈 -（1 -σ）││gk││2 and global convergence property under the general Wolfe line search con- ditions, and improve the CD method （Fletcher R, 1987, [1] ） defects. In the last part, numerical results are reported which show that the proposed method has a certain research significance by comparing with the famous CD method （Fletcher R, 1987, [1]） and the famous PRP method （Polak n,Ribire G [2], Polak B.T [3], 1969 ）.