The global convergence of the BFGS method under a modified Yuan-Wei-Lu line search technique

2019 ◽  
Vol 84 (2) ◽  
pp. 781-793
Author(s):  
Alireza Hosseini Dehmiry
Keyword(s):  
Global Convergence ◽  
Line Search ◽  
Bfgs Method ◽  
Search Technique ◽  
Line Search Technique

scholarly journals A family of global convergent inexact secant methods for nonconvex constrained optimization

2018 ◽  
Vol 12 (2) ◽  
pp. 165-176
Author(s):  
Zhujun Wang ◽  
Li Cai ◽  
Zheng Peng
Keyword(s):  
Global Convergence ◽  
Constrained Optimization ◽  
Line Search ◽  
Merit Function ◽  
Exact Penalty ◽  
Search Technique ◽  
Nonconvex Constrained Optimization ◽  
Secant Methods ◽  
Armijo Line Search ◽  
Line Search Technique

We present a family of new inexact secant methods in association with Armijo line search technique for solving nonconvex constrained optimization. Different from the existing inexact secant methods, the algorithms proposed in this paper need not compute exact directions. By adopting the nonsmooth exact penalty function as the merit function, the global convergence of the proposed algorithms is established under some reasonable conditions. Some numerical results indicate that the proposed algorithms are both feasible and effective.

scholarly journals A Limited Memory BFGS Method for Solving Large-Scale Symmetric Nonlinear Equations

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Xiangrong Li ◽  
Xiaoliang Wang ◽  
Xiabin Duan
Keyword(s):  
Nonlinear Equations ◽  
Large Scale ◽  
Line Search ◽  
Bfgs Method ◽  
Search Technique ◽  
Limited Memory Bfgs Method ◽  
Limited Memory ◽  
Line Search Technique ◽  
The Given ◽  
Derivative Information

A limited memory BFGS (L-BFGS) algorithm is presented for solving large-scale symmetric nonlinear equations, where a line search technique without derivative information is used. The global convergence of the proposed algorithm is established under some suitable conditions. Numerical results show that the given method is competitive to those of the normal BFGS methods.

scholarly journals A Trust-Region-Based BFGS Method with Line Search Technique for Symmetric Nonlinear Equations

2009 ◽  
Vol 2009 ◽  
pp. 1-22 ◽  
Author(s):  
Gonglin Yuan ◽  
Shide Meng ◽  
Zengxin Wei
Keyword(s):  
Nonlinear Equations ◽  
Line Search ◽  
Trust Region Method ◽  
Trust Region ◽  
Bfgs Method ◽  
Search Technique ◽  
Region Method ◽  
Global And Superlinear Convergence ◽  
Line Search Technique ◽  
The Given

A trust-region-based BFGS method is proposed for solving symmetric nonlinear equations. In this given algorithm, if the trial step is unsuccessful, the linesearch technique will be used instead of repeatedly solving the subproblem of the normal trust-region method. We establish the global and superlinear convergence of the method under suitable conditions. Numerical results show that the given method is competitive to the normal trust region method.

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.

scholarly journals The Number Density Evolution of Extreme Emission Line Galaxies in 3D-HST: Results from a Novel Automated Line Search Technique for Slitless Spectroscopy

2018 ◽  
Vol 854 (1) ◽  
pp. 29 ◽  
Author(s):  
Michael V. Maseda ◽  
Arjen van der Wel ◽  
Hans-Walter Rix ◽  
Ivelina Momcheva ◽  
Gabriel B. Brammer ◽  
...  
Keyword(s):  
Emission Line ◽  
Line Search ◽  
Number Density ◽  
Search Technique ◽  
Density Evolution ◽  
Line Search Technique ◽  
Emission Line Galaxies ◽  
Automated Line

A Simulated Annealing-Based Barzilai–Borwein Gradient Method for Unconstrained Optimization Problems

2019 ◽  
Vol 36 (04) ◽  
pp. 1950017 ◽  
Author(s):  
Wen-Li Dong ◽  
Xing Li ◽  
Zheng Peng
Keyword(s):  
Simulated Annealing ◽  
Unconstrained Optimization ◽  
Gradient Method ◽  
Line Search ◽  
High Efficiency ◽  
Optimization Problems ◽  
Search Technique ◽  
Unconstrained Optimization Problems ◽  
Armijo Line Search ◽  
Line Search Technique

In this paper, we propose a simulated annealing-based Barzilai–Borwein (SABB) gradient method for unconstrained optimization problems. The SABB method accepts the Barzilai–Borwein (BB) step by a simulated annealing rule. If the BB step cannot be accepted, the Armijo line search is used. The global convergence of the SABB method is established under some mild conditions. Numerical experiments indicate that, compared to some existing BB methods using nonmonotone line search technique, the SABB method performs well with high efficiency.

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