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.,...
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; ...
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 ...
newton_cgrequires the function value to compute the step size (line search) but not to compute the descent direction: online 105fvalis computed but never used. This means that we could just pass agrad_hessfunction instead offunc_grad_hess. The overhead of computing the objective value when ...
A conjugate gradient (CG)-type algorithm CG_Plan is introduced for calculating an approximate solution of Newton's equation within large-scale optimization frameworks. The approximate solution must satisfy suitable properties to ensure global convergence. In practice, the CG algorithm is widely used, ...
We propose to address this limitation with Hessian averaging: instead of using the most recent Hessian estimate, our algorithm maintains an average of all the past estimates. This reduces the stochastic noise while avoiding the computational blow-up. We show that this scheme exhibits local Q-...
We proposed an adjoint-based optimization method—a modified inexact Newton-CG algorithm—to solve the optimization problem, which was demonstrated to converge rapidly, CRediT authorship contribution statement Dingcheng Luo: Conceptualization, Investigation, Methodology, Software, Writing – original draft. ...
optimization 》 个人这篇最重要，给出了理论证明《A Linearly-Convergent Stochastic L-BFGS Algorithm》...
which uses the Hessian matrix of second derivatives to approximate the local curvature of a function. Quasi-Newton methods use approximate versions of the Hessian matrix that are updated as the algorithm proceeds. This allows the algorithm to more quickly converge to the optimum without needing to ...
(MOLFs) for training mean vector parameters .The simulation results of the proposedhybrid training algorithm on a real dataset are compared with those of the recursive least square based RBF(RLS‐RBF) and Levenberg‐Marquardt method based RBF(LM‐RBF) training algorithms .Also , the analysis of...