A Trust Region Algorithm Based on General Curve-linear Searching Direction for Unconstrained Optimization

2011 ◽  
Author(s):  
Yang Shu-ping ◽  
Yuan Xiu-gui ◽  
Liu Zai-Ming
Keyword(s):  
Unconstrained Optimization ◽  
Trust Region ◽  
Trust Region Algorithm ◽  
General Curve

scholarly journals A Novel Self-Adaptive Trust Region Algorithm for Unconstrained Optimization

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Yunlong Lu ◽  
Wenyu Li ◽  
Mingyuan Cao ◽  
Yueting Yang
Keyword(s):  
Objective Function ◽  
Unconstrained Optimization ◽  
Optimization Problems ◽  
Trust Region Method ◽  
Trust Region ◽  
Convergence Properties ◽  
Trust Region Algorithm ◽  
Unconstrained Optimization Problems ◽  
Piecewise Function ◽  
Self Adaptive

A new self-adaptive rule of trust region radius is introduced, which is given by a piecewise function on the ratio between the actual and predicted reductions of the objective function. A self-adaptive trust region method for unconstrained optimization problems is presented. The convergence properties of the method are established under reasonable assumptions. Preliminary numerical results show that the new method is significant and robust for solving unconstrained optimization problems.

scholarly journals A Filter and Nonmonotone Adaptive Trust Region Line Search Method for Unconstrained Optimization

Symmetry ◽  
2020 ◽  
Vol 12 (4) ◽  
pp. 656
Author(s):  
Quan Qu ◽  
Xianfeng Ding ◽  
Xinyi Wang
Keyword(s):  
Unconstrained Optimization ◽  
Line Search ◽  
Optimization Problems ◽  
Hessian Matrix ◽  
Trust Region ◽  
Approximate Model ◽  
Trust Region Algorithm ◽  
Unconstrained Optimization Problems ◽  
Line Search Method ◽  
Quasi Newton

In this paper, a new nonmonotone adaptive trust region algorithm is proposed for unconstrained optimization by combining a multidimensional filter and the Goldstein-type line search technique. A modified trust region ratio is presented which results in more reasonable consistency between the accurate model and the approximate model. When a trial step is rejected, we use a multidimensional filter to increase the likelihood that the trial step is accepted. If the trial step is still not successful with the filter, a nonmonotone Goldstein-type line search is used in the direction of the rejected trial step. The approximation of the Hessian matrix is updated by the modified Quasi-Newton formula (CBFGS). Under appropriate conditions, the proposed algorithm is globally convergent and superlinearly convergent. The new algorithm shows better performance in terms of the Dolan–Moré performance profile. Numerical results demonstrate the efficiency and robustness of the proposed algorithm for solving unconstrained optimization problems.

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