A Note on Wedge Trust Region Radius Update

2011 ◽  
Vol 52-54 ◽  
pp. 926-931
Author(s):  
Qing Hua Zhou ◽  
Feng Xia Xu ◽  
Yan Geng ◽  
Ya Rui Zhang
Keyword(s):  
Optimization Problems ◽  
Trust Region Method ◽  
Trust Region ◽  
Test Problems ◽  
Region Method ◽  
Derivative Free Optimization ◽  
Derivative Free ◽  
Updating Rule

Wedge trust region method based on traditional trust region is designed for derivative free optimization problems. This method adds a constraint to the trust region problem, which is called “wedge method”. The problem is that the updating strategy of wedge trust region radius is somewhat simple. In this paper, we develop and combine a new radius updating rule with this method. For most test problems, the number of function evaluations is reduced significantly. The experiments demonstrate the effectiveness of the improvement through our algorithm.

scholarly journals A Fractional Trust Region Method for Linear Equality Constrained Optimization

2016 ◽  
Vol 2016 ◽  
pp. 1-10 ◽  
Author(s):  
Honglan Zhu ◽  
Qin Ni ◽  
Liwei Zhang ◽  
Weiwei Yang
Keyword(s):  
Constrained Optimization ◽  
Optimization Problems ◽  
Null Space ◽  
Trust Region Method ◽  
Trust Region ◽  
Test Problems ◽  
Fractional Model ◽  
Region Method ◽  
Linear Equality ◽  
Space Technique

A quasi-Newton trust region method with a new fractional model for linearly constrained optimization problems is proposed. We delete linear equality constraints by using null space technique. The fractional trust region subproblem is solved by a simple dogleg method. The global convergence of the proposed algorithm is established and proved. Numerical results for test problems show the efficiency of the trust region method with new fractional model. These results give the base of further research on nonlinear optimization.

scholarly journals A wedge trust region method with self-correcting geometry for derivative-free optimization

2015 ◽  
Vol 5 (2) ◽  
pp. 169-184 ◽  
Author(s):  
Liang Zhang ◽  
◽  
Wenyu Sun ◽  
Raimundo J. B. de Sampaio ◽  
Jinyun Yuan ◽  
...  
Keyword(s):  
Trust Region Method ◽  
Trust Region ◽  
Region Method ◽  
Derivative Free Optimization ◽  
Derivative Free

Based on GA Mixed with Trust Region Method Solving Nonlinear Least Square Problems

2011 ◽  
Vol 141 ◽  
pp. 92-97
Author(s):  
Miao Hu ◽  
Tai Yong Wang ◽  
Bo Geng ◽  
Qi Chen Wang ◽  
Dian Peng Li
Keyword(s):  
Genetic Algorithm ◽  
Optimization Problems ◽  
Trust Region Method ◽  
Trust Region ◽  
Least Square ◽  
Search Range ◽  
Genetic Search ◽  
Region Method ◽  
Unconstrained Optimization Problems ◽  
Least Square Problems

Nonlinear least square is one of the unconstrained optimization problems. In order to solve the least square trust region sub-problem, a genetic algorithm (GA) of global convergence was applied, and the premature convergence of genetic algorithms was also overcome through optimizing the search range of GA with trust region method (TRM), and the convergence rate of genetic algorithm was increased by the randomness of the genetic search. Finally, an example of banana function was established to verify the GA, and the results show the practicability and precision of this algorithm.

Parameterize the Center of the Trust Region for Solving Quadratic Interpolation Models

2011 ◽  
Vol 52-54 ◽  
pp. 920-925
Author(s):  
Qing Hua Zhou ◽  
Yan Geng ◽  
Ya Rui Zhang ◽  
Feng Xia Xu
Keyword(s):  
Optimization Problems ◽  
Trust Region Method ◽  
Main Idea ◽  
Trust Region ◽  
Search Region ◽  
Trust Region Algorithm ◽  
Unconstrained Optimization Problems ◽  
Simplex Search ◽  
Quadratic Interpolation ◽  
Derivative Free

The derivative free trust region algorithm was considered for solving the unconstrained optimization problems. This paper introduces a novel methodology that modified the center of the trust region in order to improve the search region. The main idea is parameterizing the center of the trust region based on the ideas of multi-directional search and simplex search algorithms. The scope of the new region was so expanded by introducing a parameter as to we can find a better descent directions. Experimental results reveal that the new method is more effective than the classic trust region method on the testing problems.

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.

scholarly journals AN IMPROVED ADAPTIVE TRUST-REGION METHOD FOR UNCONSTRAINED OPTIMIZATION

2014 ◽  
Vol 19 (4) ◽  
pp. 469-490 ◽  
Author(s):  
Hamid Esmaeili ◽  
Morteza Kimiaei
Keyword(s):  
Unconstrained Optimization ◽  
Large Scale ◽  
Optimization Problems ◽  
Trust Region Method ◽  
Trust Region ◽  
Standard Test ◽  
Test Problems ◽  
Unconstrained Optimization Problems ◽  
Large Scale Problems ◽  
Adaptive Radius

In this study, we propose a trust-region-based procedure to solve unconstrained optimization problems that take advantage of the nonmonotone technique to introduce an efficient adaptive radius strategy. In our approach, the adaptive technique leads to decreasing the total number of iterations, while utilizing the structure of nonmonotone formula helps us to handle large-scale problems. The new algorithm preserves the global convergence and has quadratic convergence under suitable conditions. Preliminary numerical experiments on standard test problems indicate the efficiency and robustness of the proposed approach for solving unconstrained optimization problems.

A Sequential Linear Programming Coordination Algorithm for Analytical Target Cascading

2010 ◽  
Vol 132 (2) ◽  
Author(s):  
Jeongwoo Han ◽  
Panos Y. Papalambros
Keyword(s):  
Design Optimization ◽  
Optimization Problems ◽  
Trust Region Method ◽  
Trust Region ◽  
Test Problems ◽  
Analytical Target Cascading ◽  
Step Size ◽  
Coordination Strategy ◽  
Target Cascading ◽  
Solution Accuracy

Decomposition-based strategies, such as analytical target cascading (ATC), are often employed in design optimization of complex systems. Achieving convergence and computational efficiency in the coordination strategy that solves the partitioned problem is a key challenge. A new convergent strategy is proposed for ATC that coordinates interactions among subproblems using sequential linearizations. The linearity of subproblems is maintained using infinity norms to measure deviations between targets and responses. A subproblem suspension strategy is used to suspend temporarily inclusion of subproblems that do not need significant redesign, based on trust region and target value step size. An individual subproblem trust region method is introduced for faster convergence. The proposed strategy is intended for use in design optimization problems where sequential linearizations are typically effective, such as problems with extensive monotonicities, a large number of constraints relative to variables, and propagation of probabilities with normal distributions. Experiments with test problems show that, relative to standard ATC coordination, the number of subproblem evaluations is reduced considerably while the solution accuracy depends on the degree of monotonicity and nonlinearity.

A new self-adaptive trust region method for unconstrained optimization

2011 ◽  
Vol 18 (9) ◽  
pp. 1303-1309 ◽  
Author(s):  
Zhaocheng Cui ◽  
Boying Wu
Keyword(s):  
Unconstrained Optimization ◽  
Superlinear Convergence ◽  
Optimization Problems ◽  
Trust Region Method ◽  
Trust Region ◽  
Convergence Properties ◽  
Region Method ◽  
Unconstrained Optimization Problems ◽  
Global And Superlinear Convergence ◽  
Self Adaptive

In this paper, we propose a new self-adaptive trust region method for unconstrained optimization problems and develop some convergence properties. In our algorithm, we use the previous and current iterative information to define a suitable trust region radius at each iteration. The global and superlinear convergence properties of the algorithm are established under reasonable assumptions. Preliminary numerical results show that the new method is efficient and attractive for solving unconstrained optimization problems.

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