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.

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.

scholarly journals A Nonmonotone Weighting Self-Adaptive Trust Region Algorithm for Unconstrained Nonconvex Optimization

2015 ◽  
Vol 2015 ◽  
pp. 1-8
Author(s):  
Yunlong Lu ◽  
Weiwei Yang ◽  
Wenyu Li ◽  
Xiaowei Jiang ◽  
Yueting Yang
Keyword(s):  
Nonconvex Optimization ◽  
Line Search ◽  
Optimization Problems ◽  
Trust Region Method ◽  
Trust Region ◽  
Search Technique ◽  
Trust Region Algorithm ◽  
Unconstrained Optimization Problems ◽  
Line Search Technique ◽  
Self Adaptive

A new trust region method is presented, which combines nonmonotone line search technique, a self-adaptive update rule for the trust region radius, and the weighting technique for the ratio between the actual reduction and the predicted reduction. Under reasonable assumptions, the global convergence of the method is established for unconstrained nonconvex optimization. Numerical results show that the new method is efficient and robust for solving unconstrained optimization problems.

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.

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.

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.

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