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 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 Stochastic Trust Region Method for Unconstrained Optimization Problems

2019 ◽  
Vol 2019 ◽  
pp. 1-10
Author(s):  
Ningning Li ◽  
Dan Xue ◽  
Wenyu Sun ◽  
Jing Wang
Keyword(s):  
Objective Function ◽  
Optimization Problems ◽  
Trust Region Method ◽  
Trust Region ◽  
Unconstrained Minimization ◽  
Quadratic Model ◽  
Convergence Properties ◽  
Region Method ◽  
Unconstrained Optimization Problems

In this paper, a stochastic trust region method is proposed to solve unconstrained minimization problems with stochastic objectives. Particularly, this method can be used to deal with nonconvex problems. At each iteration, we construct a quadratic model of the objective function. In the model, stochastic gradient is used to take the place of deterministic gradient for both the determination of descent directions and the approximation of the Hessians of the objective function. The behavior and the convergence properties of the proposed method are discussed under some reasonable conditions. Some preliminary numerical results show that our method is potentially efficient.

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