A new trust-region method with line search for solving symmetric nonlinear equations

2011 ◽  
Vol 88 (10) ◽  
pp. 2109-2123 ◽  
Author(s):  
Gonglin Yuan ◽  
Sha Lu ◽  
Zengxin Wei
Keyword(s):  
Nonlinear Equations ◽  
Line Search ◽  
Trust Region Method ◽  
Trust Region ◽  
Region Method

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.

A BFGS trust-region method for nonlinear equations

Computing ◽  
2011 ◽  
Vol 92 (4) ◽  
pp. 317-333 ◽  
Author(s):  
Gonglin Yuan ◽  
Zengxin Wei ◽  
Xiwen Lu
Keyword(s):  
Nonlinear Equations ◽  
Trust Region Method ◽  
Trust Region ◽  
Region Method

Nonmonotone conic trust region method with line search technique for bound constrained optimization

2019 ◽  
Vol 53 (3) ◽  
pp. 787-805
Author(s):  
Lijuan Zhao
Keyword(s):  
Constrained Optimization ◽  
Line Search ◽  
Optimization Problems ◽  
Trust Region Method ◽  
Trust Region ◽  
Affine Scaling ◽  
Search Technique ◽  
Region Method ◽  
Bound Constrained Optimization ◽  
Line Search Technique

In this paper, we propose a nonmonotone trust region method for bound constrained optimization problems, where the bounds are dealt with by affine scaling technique. Differing from the traditional trust region methods, the subproblem in our algorithm is based on a conic model. Moreover, when the trial point isn’t acceptable by the usual trust region criterion, a line search technique is used to find an acceptable point. This procedure avoids resolving the trust region subproblem, which may reduce the total computational cost. The global convergence and Q-superlinear convergence of the algorithm are established under some mild conditions. Numerical results on a series of standard test problems are reported to show the effectiveness of the new method.

Sign in / Sign up

Export Citation Format

Share Document