A Nonmonotone Line Search Technique for Newton’s Method

1986 ◽  
Vol 23 (4) ◽  
pp. 707-716 ◽  
Author(s):  
L. Grippo ◽  
F. Lampariello ◽  
S. Lucidi
Keyword(s):  
Newton’S Method ◽  
Newton's Method ◽  
Line Search ◽  
Nonmonotone Line Search ◽  
Search Technique ◽  
Line Search Technique

scholarly journals THE BARZILAI AND BORWEIN GRADIENT METHOD WITH NONMONOTONE LINE SEARCH FOR NONSMOOTH CONVEX OPTIMIZATION PROBLEMS

2012 ◽  
Vol 17 (2) ◽  
pp. 203-216 ◽  
Author(s):  
Gonglin Yuan ◽  
Zengxin Wei
Keyword(s):  
Line Search ◽  
Optimization Problems ◽  
Nonmonotone Line Search ◽  
Gradient Algorithm ◽  
Search Technique ◽  
Nonsmooth Problems ◽  
Smooth Optimization ◽  
Line Search Technique ◽  
Nonsmooth Convex Minimization ◽  
The Given

The Barzilai and Borwein gradient algorithm has received a great deal of attention in recent decades since it is simple and effective for smooth optimization problems. Whether can it be extended to solve nonsmooth problems? In this paper, we answer this question positively. The Barzilai and Borwein gradient algorithm combined with a nonmonotone line search technique is proposed for nonsmooth convex minimization. The global convergence of the given algorithm is established under suitable conditions. Numerical results show that this method is efficient.

scholarly journals An Adaptive Nonmonotone Line Search Technique for Solving Systems of Nonlinear Equations

2021 ◽  
Vol 2021 ◽  
pp. 1-6
Author(s):  
Masoud Hatamian ◽  
Mahmoud Paripour ◽  
Farajollah Mohammadi Yaghoobi ◽  
Nasrin Karamikabir
Keyword(s):  
Global Convergence ◽  
Nonlinear Equations ◽  
Line Search ◽  
Nonmonotone Line Search ◽  
Systems Of Nonlinear Equations ◽  
System Of Nonlinear Equations ◽  
Search Technique ◽  
Numerical Examples ◽  
Line Search Technique ◽  
Novel Algorithm

In this article, a new nonmonotone line search technique is proposed for solving a system of nonlinear equations. We attempt to answer this question how to control the degree of the nonmonotonicity of line search rules in order to reach a more efficient algorithm? Therefore, we present a novel algorithm that can avoid the increase of unsuccessful iterations. For this purpose, we show the robust behavior of the proposed algorithm by solving a few numerical examples. Under some suitable assumptions, the global convergence of our strategy is proved.

scholarly journals A Nonmonotone Weighting Self-Adaptive Trust Region Algorithm for Unconstrained Nonconvex Optimization

2015 ◽  
Vol 2015 ◽  
pp. 1-8
Author(s):  
Yunlong Lu ◽  
Weiwei Yang ◽  
Wenyu Li ◽  
Xiaowei Jiang ◽  
Yueting Yang
Keyword(s):  
Nonconvex Optimization ◽  
Line Search ◽  
Optimization Problems ◽  
Trust Region Method ◽  
Trust Region ◽  
Search Technique ◽  
Trust Region Algorithm ◽  
Unconstrained Optimization Problems ◽  
Line Search Technique ◽  
Self Adaptive

A new trust region method is presented, which combines nonmonotone line search technique, a self-adaptive update rule for the trust region radius, and the weighting technique for the ratio between the actual reduction and the predicted reduction. Under reasonable assumptions, the global convergence of the method is established for unconstrained nonconvex optimization. Numerical results show that the new method is efficient and robust for solving unconstrained optimization problems.

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