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 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 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 Improved Line Search Filter Method for the System of Nonlinear Equations

2012 ◽  
Vol 2012 ◽  
pp. 1-15 ◽  
Author(s):  
Zhong Jin ◽  
Yuqing Wang
Keyword(s):  
Global Convergence ◽  
Objective Function ◽  
Nonlinear Equations ◽  
Numerical Experiments ◽  
Line Search ◽  
Equality Constraints ◽  
Filter Method ◽  
System Of Nonlinear Equations ◽  
Search Filter

An improved line search filter algorithm for the system of nonlinear equations is presented. We divide the equations into two groups, one contains the equations that are treated as equality constraints and the square of other equations is regarded as objective function. Two groups of equations are updated at every iteration in the works by Nie (2004, 2006, and 2006), by Nie et al. (2008), and by Gu (2011), while we just update them at the iterations when it is needed indeed. As a consequence, the scale of the calculation is decreased in a certain degree. Under some suitable conditions the global convergence can be induced. In the end, numerical experiments show that the method in this paper is effective.

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