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1.
《高等学校计算数学学报》2016,(2)
The trust region(TR) method for optimization is a class of effective methods.The conic model can be regarded as a generalized quadratic model and it possesses the good convergence properties of the quadratic model near the minimizer.The Barzilai and Borwein(BB) gradient method is also an effective method,it can be used for solving large scale optimization problems to avoid the expensive computation and storage of matrices.In addition,the BB stepsize is easy to determine without large computational efforts.In this paper,based on the conic trust region framework,we employ the generalized BB stepsize,and propose a new nonmonotone adaptive trust region method based on simple conic model for large scale unconstrained optimization.Unlike traditional conic model,the Hessian approximation is an scalar matrix based on the generalized BB stepsize,which resulting a simple conic model.By adding the nonmonotone technique and adaptive technique to the simple conic model,the new method needs less storage location and converges faster.The global convergence of the algorithm is established under certain conditions.Numerical results indicate that the new method is effective and attractive for large scale unconstrained optimization problems. 相似文献
2.
Zhaocheng Cui Boying WuShaojian Qu 《Journal of Computational and Applied Mathematics》2011,235(8):2432-2441
In this paper, we propose a trust region method for unconstrained optimization that can be regarded as a combination of conic model, nonmonotone and line search techniques. Unlike in traditional trust region methods, the subproblem of our algorithm is the conic minimization subproblem; moreover, our algorithm performs a nonmonotone line search to find the next iteration point when a trial step is not accepted, instead of resolving the subproblem. The global and superlinear convergence results for the algorithm are established under reasonable assumptions. Numerical results show that the new method is efficient for unconstrained optimization problems. 相似文献
3.
In this paper, we present a nonmonotone adaptive trust region method for unconstrained optimization based on conic model. The new method combines nonmonotone technique and a new way to determine trust region radius at each iteration. The local and global convergence properties are proved under reasonable assumptions. Numerical experiments show that our algorithm is effective. 相似文献
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Jinhua Fu Wenyu Sun Raimundo J. B. De Sampaio 《Journal of Applied Mathematics and Computing》2005,19(1-2):165-177
In this paper, an adaptive trust region method based on the conic model for unconstrained optimization problems is proposed and analyzed. We establish the global and superlinear convergence results of the method. Numerical tests are reported that confirm the efficiency of the new method. 相似文献
6.
In this paper, we present an adaptive trust region method for solving unconstrained optimization problems which combines nonmonotone technique with a new update rule for the trust region radius. At each iteration, our method can adjust the trust region radius of related subproblem. We construct a new ratio to adjust the next trust region radius which is different from the ratio in the traditional trust region methods. The global and superlinear convergence results of the method are established under reasonable assumptions. Numerical results show that the new method is efficient for unconstrained optimization problems. 相似文献
7.
A new trust region method with adaptive radius 总被引:2,自引:0,他引:2
In this paper we develop a new trust region method with adaptive radius for unconstrained optimization problems. The new method
can adjust the trust region radius automatically at each iteration and possibly reduces the number of solving subproblems.
We investigate the global convergence and convergence rate of this new method under some mild conditions. Theoretical analysis
and numerical results show that the new adaptive trust region radius is available and reasonable and the resultant trust region
method is efficient in solving practical optimization problems.
The work was supported in part by NSF grant CNS-0521142, USA. 相似文献
8.
In this paper, based on a simple model of trust region sub-problem, we combine the trust region method with the non-monotone and self-adaptive techniques to propose a new non-monotone self-adaptive trust region algorithm for unconstrained optimization. By use of the simple model, the new method needs less memory capacitance, computational complexity and CPU time. The convergence results of the method are proved under certain conditions. Numerical results show that the new method is effective and attractive for large-scale optimization problems. 相似文献
9.
王承竞 《高校应用数学学报(英文版)》2006,21(3)
Trust region methods are powerful and effective optimization methods. The conic model method is a new type of method with more information available at each iteration than standard quadratic-based methods. The advantages of the above two methods can be combined to form a more powerful method for constrained optimization. The trust region subproblem of our method is to minimize a conic function subject to the linearized constraints and trust region bound. At the same time, the new algorithm still possesses robust global properties. The global convergence of the new algorithm under standard conditions is established. 相似文献
10.
Wang Chengjing 《高校应用数学学报(英文版)》2006,21(3):263-275
Trust region methods are powerful and effective optimization methods.The conic model method is a new type of method with more information available at each iteration than standard quadratic-based methods.The advantages of the above two methods can be combined to form a more powerful method for constrained optimization.The trust region subproblem of our method is to minimize a conic function subject to the linearized constraints and trust region bound.At the same time,the new algorithm still possesses robust global properties.The global convergence of the new algorithm under standard conditions is established. 相似文献
11.
In this paper, we propose a new trust region method for unconstrained optimization problems. The new trust region method can automatically adjust the trust region radius of related subproblems at each iteration and has strong global convergence under some mild conditions. We also analyze the global linear convergence, local superlinear and quadratic convergence rate of the new method. Numerical results show that the new trust region method is available and efficient in practical computation. 相似文献
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解线性约束优化问题的新锥模型信赖域法 总被引:1,自引:0,他引:1
本文提出了一个解线性等式约束优化问题的新锥模型信赖域方法.论文采用零空间技术消除了新锥模型子问题中的线性等式约束,用折线法求解转换后的子问题,并给出了解线性等式约束优化问题的信赖域方法.论文提出并证明了该方法的全局收敛性,并给出了该方法解线性等式约束优化问题的数值实验.理论和数值实验结果表明新锥模型信赖域方法是有效的,这给出了用新锥模型进一步研究非线性优化的基础. 相似文献
13.
In this paper, a new derivative free trust region method is developed basedon the conic interpolation model for the unconstrained optimization. The conic inter-polation model is built by means of the quadratic model function, the collinear scalingformula, quadratic approximation and interpolation. All the parameters in this model axedetermined by objective function interpolation condition. A new derivative free method isdeveloped based upon this model and the global convergence of this new method is provedwithout any information on gradient. 相似文献
14.
一类带非单调线搜索的信赖域算法 总被引:1,自引:0,他引:1
通过将非单调Wolfe线搜索技术与传统的信赖域算法相结合,我们提出了一类新的求解无约束最优化问题的信赖域算法.新算法在每一迭代步只需求解一次信赖域子问题,而且在每一迭代步Hesse阵的近似都满足拟牛顿条件并保持正定传递.在一定条件下,证明了算法的全局收敛性和强收敛性.数值试验表明新算法继承了非单调技术的优点,对于求解某... 相似文献
15.
本文对无约束优化问题提出了一类基于锥模型的非单调信赖域算法.二次模型非单调信赖域算法是新算法的特例.在适当的条件下,证明了算法的全局收敛性及Q-二次收敛性. 相似文献
16.
Based on simple quadratic models of the trust region subproblem, we combine the trust region method with the nonmonotone and adaptive techniques to propose a new nonmonotone adaptive trust region algorithm for unconstrained optimization. Unlike traditional trust region method, our trust region subproblem is very simple by using a new scale approximation of the minimizing function??s Hessian. The new method needs less memory capacitance and computational complexity. The convergence results of the method are proved under certain conditions. Numerical results show that the new method is effective and attractive for large scale unconstrained problems. 相似文献
17.
Trust-region methods are powerful optimization methods. The conic model method is a new type of method with more information available at each iteration than standard quadratic-based methods. Can we combine their advantages to form a more powerful method for constrained optimization? In this paper we give a positive answer and present a conic trust-region algorithm for non-linearly constrained optimization problems. The trust-region subproblem of our method is to minimize a conic function subject to the linearized constraints and the trust region bound. The use of conic functions allows the model to interpolate function values and gradient values of the Lagrange function at both the current point and previous iterate point. Since conic functions are the extension of quadratic functions, they approximate general nonlinear functions better than quadratic functions. At the same time, the new algorithm possesses robust global properties. In this paper we establish the global convergence of the new algorithm under standard conditions. 相似文献
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Wen-yuSun Jin-yunYuan Ya-xiangYuan 《计算数学(英文版)》2003,21(3):295-304
In this paper we present a trust region method of conic model for linearly constrained optimization problems.We discuss trust region approaches with conic model subproblems.Some equivalent variation properties and optimality conditions are given.A trust region algorithm based on conic model is constructed.Global convergence of the method is established. 相似文献
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