A derivative-free affine scaling trust region methods based on probabilistic models with new nonmonotone line search technique for linear inequality constrained minimization without strict complementarity

2018 ◽  
Vol 96 (4) ◽  
pp. 663-691
Author(s):  
Peng Wang ◽  
Detong Zhu
Keyword(s):  
Line Search ◽  
Linear Inequality ◽  
Probabilistic Models ◽  
Trust Region ◽  
Affine Scaling ◽  
Trust Region Methods ◽  
Search Technique ◽  
Strict Complementarity ◽  
Derivative Free ◽  
Line Search Technique

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.

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 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.

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