一种新的非线性共轭梯度法的全局收敛性

Global Convergence Properties of a New Class of Nonlinear Conjugate Gradient Methods

关键词:  无约束优化  共轭梯度  全局收敛性  Wolfe线搜索

Key words:  unconstrained optimization  conjugate gradient  global convergence  Wolf line search

摘要:

基于标准Wolfe线搜索条件,提出一种新的线搜索:T_k满足
f(x_k+T_kd_k)-f(x_k)≤ max{WT_kg_k^Td_k,-VT_k²‖d_k‖²}和g(x_k+T_kd_k)^Td_k ≥ max{^eg_k^Td_k,-2^eT_k‖d_k‖²},并在此基础上给出了一种新的非线性共轭梯度算法及其全局收敛性定理.

Abstract:

A new line search based on the standard Wolfe line search conditions α_k satisfing
f(x_k+T_kd_k)-f(x_k) ≤ max{WT_kg_k^Td_k,-VT_k²‖d_k‖²} and g(x_k+T_kd_k)^Td_k ≥ max{^eg_k^Td_k,-2^eT_k‖d_k‖²},was present in this paper,and the global convergence of a new class of nonlinear conjugate gradient methods with the new line search was given.