【摘要】 <正> 1.引言 考虑无约束优化问题: (p) f(x),其中f(x):Rn→R1是一阶连续可微函数.求解问题(P)的共轭梯度法,收敛速度快,存储量小,适于求解大规模问题.记gk=(?)f(xk)它具有如下迭代公式形式更多还原

【Abstract】 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 Rn without assuming that the sequence {xk}of iterates is bounded. We prove that the limit infimum of ||V/(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||→∞, argmin{f(x) : x ∈ Rn} = φ, and f(xk) ↓inf{f(x) : x ∈ Rn}. Combining FR, PR, HS methods with our new method, FR, PR, HS methods are modified to have global convergence property. Numerical result show that the new algorithms are efficient by comparing with FR, PR, HS conjugate gradient methods with Armijo step size rule.更多还原