Nonmonotone trust region method for solving optimization problems

2004 ◽  
Vol 156 (1) ◽  
pp. 159-174 ◽  
Author(s):  
Wenyu Sun
Keyword(s):  
Optimization Problems ◽  
Trust Region Method ◽  
Trust Region ◽  
Region Method

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.

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.

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.

scholarly journals A Nonmonotone Adaptive Trust Region Method Based on Conic Model for Unconstrained Optimization

2014 ◽  
Vol 2014 ◽  
pp. 1-8
Author(s):  
Zhaocheng Cui
Keyword(s):  
Unconstrained Optimization ◽  
Optimization Problems ◽  
Trust Region Method ◽  
Trust Region ◽  
New Method ◽  
Convergence Properties ◽  
Initial Trust ◽  
Conic Model ◽  
Region Method ◽  
Unconstrained Optimization Problems

We propose a nonmonotone adaptive trust region method for unconstrained optimization problems which combines a conic model and a new update rule for adjusting the trust region radius. Unlike the traditional adaptive trust region methods, the subproblem of the new method is the conic minimization subproblem. Moreover, at each iteration, we use the last and the current iterative information to define a suitable initial trust region radius. The global and superlinear convergence properties of the proposed method are established under reasonable conditions. Numerical results show that the new method is efficient and attractive for unconstrained optimization problems.

COMBINATION ADAPTIVE TRUST REGION METHOD BY NON-MONOTONE STRATEGY FOR UNCONSTRAINED NONLINEAR PROGRAMMING

2011 ◽  
Vol 28 (05) ◽  
pp. 585-600 ◽  
Author(s):  
KEYVAN AMINI ◽  
MASOUD AHOOKHOSH
Keyword(s):  
Nonlinear Programming ◽  
Quadratic Convergence ◽  
Optimization Problems ◽  
Trust Region Method ◽  
Trust Region ◽  
Trust Region Algorithm ◽  
Region Method ◽  
Unconstrained Optimization Problems ◽  
Adaptive Technique ◽  
And Function

In this paper, we present a new trust region method for unconstrained nonlinear programming in which we blend adaptive trust region algorithm by non-monotone strategy to propose a new non-monotone trust region algorithm with automatically adjusted radius. Both non-monotone strategy and adaptive technique can help us introduce a new algorithm that reduces the number of iterations and function evaluations. The new algorithm preserves the global convergence and has local superlinear and quadratic convergence under suitable conditions. Numerical experiments exhibit that the new trust region algorithm is very efficient and robust for unconstrained optimization problems.

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.

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.

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