结合广义Armijo步长搜索的一类新的三项共轭梯度算法及其收敛特征

作     者：孙清滢 刘新海 

作者机构：大连理工大学应用数学系辽宁大连116024 石油大学应用数学系山东东营257062 

出 版 物：《计算数学》 (Mathematica Numerica Sinica)

年 卷 期：2004年第26卷第1期

页      面：25-36页

核心收录：

学科分类：12[管理学] 1201[管理学-管理科学与工程(可授管理学、工学学位)] 07[理学] 070105[理学-运筹学与控制论] 0701[理学-数学] 

基　　金：国家自然科学基金(10171055)资助项目 

主　　题：广义Armijo步长搜索 三项共轭梯度算法 收敛特征 非线性规划 

摘      要：In this paper, we consider the convergence properties of a new class of three terms conjugate gradient methods with generalized Armijo step size rule for minimizing a continuously differentiable function f on R^π without assuming that the sequence {xk} of iterates is bounded. We prove that the limit infimum of ‖↓△f(xk)‖ is Zero. Moreover, we prove that, when f(x) is pseudo-convex (quasi-convex) function, this new method has strong convergence results: either xk→x* and x* is a minimizer (stationary point); or ‖xk‖→∞, arg min{f(x) :x∈R^n} =φ, and.f(xk) ↓ inf(f(x) : x∈R^n}. Combining FR, PR, HS methods with our new method, FR, PR, HS methods are modified to have global convergence *** result show that the new algorithms are efficient by comparing with FR,PR, HS conjugate gradient methods with Armijo step size rule.