Curvilinear path and trust region in unconstrained optimization: A convergence analysis

1987 ◽  
pp. 82-101 ◽  
Author(s):  
J. P. Bulteau ◽  
J. P. Vial
Keyword(s):  
Convergence Analysis ◽  
Unconstrained Optimization ◽  
Trust Region

scholarly journals On memory gradient method with trust region for unconstrained optimization

2005 ◽  
Vol 41 (2) ◽  
pp. 173-196 ◽  
Author(s):  
Zhen-Jun Shi ◽  
Jie Shen
Keyword(s):  
Unconstrained Optimization ◽  
Gradient Method ◽  
Trust Region ◽  
Memory Gradient Method

A randomized nonmonotone adaptive trust region method based on the simulated annealing strategy for unconstrained optimization

2019 ◽  
Vol 12 (3) ◽  
pp. 389-399
Author(s):  
Saman Babaie-Kafaki ◽  
Saeed Rezaee
Keyword(s):  
Simulated Annealing ◽  
Unconstrained Optimization ◽  
Optimization Problems ◽  
Trust Region Method ◽  
Trust Region ◽  
Test Problems ◽  
Content Type ◽  
Unconstrained Optimization Problems ◽  
Randomization Scheme ◽  
Enhance Efficiency

PurposeThe purpose of this paper is to employ stochastic techniques to increase efficiency of the classical algorithms for solving nonlinear optimization problems.Design/methodology/approachThe well-known simulated annealing strategy is employed to search successive neighborhoods of the classical trust region (TR) algorithm.FindingsAn adaptive formula for computing the TR radius is suggested based on an eigenvalue analysis conducted on the memoryless Broyden-Fletcher-Goldfarb-Shanno updating formula. Also, a (heuristic) randomized adaptive TR algorithm is developed for solving unconstrained optimization problems. Results of computational experiments on a set of CUTEr test problems show that the proposed randomization scheme can enhance efficiency of the TR methods.Practical implicationsThe algorithm can be effectively used for solving the optimization problems which appear in engineering, economics, management, industry and other areas.Originality/valueThe proposed randomization scheme improves computational costs of the classical TR algorithm. Especially, the suggested algorithm avoids resolving the TR subproblems for many times.

A new trust region method with adaptive radius for unconstrained optimization

2012 ◽  
Vol 27 (3) ◽  
pp. 419-429 ◽  
Author(s):  
Zhaocheng Cui ◽  
Boying Wu
Keyword(s):  
Unconstrained Optimization ◽  
Trust Region Method ◽  
Trust Region ◽  
Region Method ◽  
Adaptive Radius

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.

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