基于非线性尺度不变性的CCG法

１．引言 ＣＧ法对于变量个数很多的问题，是很有用的．１９７０年后它有了许多改进和发展，ＣＣＧ法以正定圆锥函数为基础［１］，它的一般方法是：设圆锥函数为 ２］其中： Ｖ＝ Ｖ（ｘ）＝１＋ ａＴｘ ≠ ０；， ｒ ∈Ｒ１为常量； ａ，ｇ ∈ Ｒｎ为常向量；ｘ ∈ Ｒｎ为变向量；Ａ∈Ｒｎ×ｎ为对称正定矩阵．算法［１］：预先给出初始近似点ｘ０∈ Ｒｎ及初始搜索方向 ｐ０；满足：其中“Ｉ”是单位矩阵， Ｖ０＝ Ｖ（ｘ０）＝ １＋ ａｔｘ０及记号“”是函数的梯度．迭代格式为： ｘｋ＋１＝ ｘｋ ＋λｋｐｋ，ｋ＝ ０，１，２，…（３…

A CCG METHOD IN VIEW OF INVARIANCY TO NONLINEAR SCALING

In this paper, a conjugate-gradient method of invariancy to nonlinear scaling with respect to a conic function is proposed. This method may be used in the minimizer of a larger class of functions in a finite number of iterations, and this class of functions is more general than class of functions using the conjugate-gradient method of a conic function (to denote simply CCG)1] to find its minimzer. In fact, this method is the extension of the CCG method. The results of the numerical evaluation show that the new method has a great effect.