Newton-CG:这种方法使用牛顿法的框架,需要计算Hessian矩阵或其逆矩阵。然而,直接计算和存储整个Hessian矩阵非常昂贵,尤其是在变量数量很多的情况下。因此,Newton-CG采用共轭梯度法来近似求解Hessian矩阵的逆方向的乘积,从而避免了直接计算Hessian矩阵。 L-BFGS:L-BFGS是一种改良的拟牛顿方法,它不直接使用Hessian矩阵,而是...
如何理解newton-cg算法？Newton-CG啊，其实挺简单的。传统的牛顿法是每一次迭代都要求Hessian矩阵的逆，...
性方程组求解问题提出了一种改进的算法——Newton-CG 算法。 关键词:数值分析;非线性方程组;Newton-CG 算法 中图分类号:O Numerrical optimization and nonlinear equations Hou Lin 1 , Shang Xiaoji 2 , Liu Liyu 1 , Yang Ying 1(1. Department of Mathmati cs,JiangSu XuZhou 221008; ...
Newton-CGnonconvex optimizationinexact gradientinexact HessianWe consider variants of a recently developed Newton-CG algorithm for nonconvex problems (Royer, C. W. & Wright, S. J. (2018) Complexity analysis of second-order line-search algorithms for smooth nonconvex optimization. SIAM J. Optim.,...
基于Newton法改进的BFGS迭代算法与Newton-CG算法 欧谦宁 【摘要】本文主要研究了数值分析中数值优化与非线性方程组求解这两个重要问题.文中首先概述了数值优化与非线性方程组的关系,然后对BFGS法的算法公式进行了改进,并对非线性方程组求解问题提出了一种改进的算法--Newton-CG算法. 【期刊名称】《赤峰学院学报(自然...
newton_cg requires the function value to compute the step size (line search) but not to compute the descent direction: on line 105 fval is computed but never used. This means that we could just pass a grad_hess function instead of func_g...
The intercept method is a Newton-type iterative approach for solving inverse singu- lar value problems originally given by M. Chu [SIAM J. Numer. Anal., 29 (1992), pp. 885-903]. When the problem is large, one may employ iterative methods to solve the Jacobian equations. However, ...
摘要: 本文主要研究了数值分析中数值优化与非线性方程组求解这两个重要问题.文中首先概述了数值优化与非线性方程组的关系,然后对BFGS法的算法公式进行了改进,并对非线性方程组求解问题提出了一种改进的算法——Newton-CG算法.关键词:数值分析 非线性方程组 Newton-CG算法 ...
本论文中,利用了Newton-CG的增广拉格朗日方法求解凸二次约束二次半定规划(convex quadratically constrained quadratic semidefinite programs(CQCQSDP))为了分析该算法的局部收敛性,我们给出了巧1在原点的Lipschitz连续性以及等价条件;得到了凸二次约束二次半定规划的Robinson约束规范,强二阶充分条件,约束非退化准则的显式...
The basic idea of this method is to apply the majorized semismooth Newton-CG augmented Lagrangian method to the primal convex problem. And we take two special nonlinear semidefinite programming problems as examples to illustrate the algorithm. Furthermore, we establish the global convergence and the ...