Practical methods of optimization; (2nd ed.)
Practical methods of optimization; (2nd ed.)
Global convergence result for conjugate gradient methods
Journal of Optimization Theory and Applications
Optimization: algorithms and consistent approximations
Optimization: algorithms and consistent approximations
A globally convergent version of the Polak-Ribière conjugate gradient method
Mathematical Programming: Series A and B
A class of gradient unconstrained minimization algorithms with adaptive stepsize
Journal of Computational and Applied Mathematics
A Nonlinear Conjugate Gradient Method with a Strong Global Convergence Property
SIAM Journal on Optimization
Introduction to Global Optimization (Nonconvex Optimization and Its Applications)
Introduction to Global Optimization (Nonconvex Optimization and Its Applications)
Convergence of memory gradient methods
International Journal of Computer Mathematics
A new trust region method with adaptive radius
Computational Optimization and Applications
The convergence of subspace trust region methods
Journal of Computational and Applied Mathematics
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In this paper, a new gradient-related algorithm for solving large-scale unconstrained optimization problems is proposed. The new algorithm is a kind of line search method. The basic idea is to choose a combination of the current gradient and some previous search directions as a new search direction and to find a step-size by using various inexact line searches. Using more information at the current iterative step may improve the performance of the algorithm. This motivates us to find some new gradient algorithms which may be more effective than standard conjugate gradient methods. Uniformly gradient-related conception is useful and it can be used to analyze global convergence of the new algorithm. The global convergence and linear convergence rate of the new algorithm are investigated under diverse weak conditions. Numerical experiments show that the new algorithm seems to converge more stably and is superior to other similar methods in many situations.