一个解界约束非线性方程组的无导数回溯线搜索仿射内点信赖域方法（英文）

文章给出了一个求解界约束非线性方程组的无导数回溯线搜索仿射内点信赖域方法.该方法利用非线性方程组的特点,对方程组中每一个函数建立插值模型.通过利用信赖域模型和回溯先搜索技术的结合,利用插值信赖域子问题子问题求解搜索方向,并利用回溯先搜索技术保证可行性.在合理的假设条件下,证明了算法的全局和快速局部收敛性.并且,通过数值实验表明该种无导数算法对求解界约束非线性方程组问题是有效的.     

基于增广Lagrange函数的约束优化问题的一个信赖域方法

本文提出一个求解不等式约束优化问题的基于指数型增广Lagrange函数的信赖域方法.基于指数型增广Lagrange函数,将传统的增广Lagrange方法的精确求解子问题转化为一个信赖域子问题,从而减少了计算量,并建立相应的信赖域算法.在一定的假设条件下,证明了算法的全局收敛性,并给出相应经典算例的数值实验结果.     

解新锥模型信赖域子问题的折线法

本文以新锥模型信赖域子问题的最优性条件为理论基础,认真讨论了新子问题的锥函数性质,分析了此函数在梯度方向及与牛顿方向连线上的单调性.在此基础上本文提出了一个求解新锥模型信赖域子问题折线法,并证明了这一子算法保证解无约束优化问题信赖域法全局收敛性要满足的下降条件.本文获得的数值实验表明该算法是有效的.     

解无约束优化问题的一个新的带线搜索的信赖域算法

在传统信赖域方法的基础上, 提出了求解无约束最优化问题的一个新的带线搜索的信赖域算法. 该算法采用大步长 Armijo 线搜索技术获得迭代步长, 克服了每次迭代求解信赖域子问题时计算量较大的缺点, 因而适用于求解大型的优化问题. 在适当的条件下, 我们证明了算法的全局收敛性. 数值实验结果表明本文所提出的算法是有效的.     

结合有效集和多维滤子技术的拟Newton信赖域算法(英文)

针对界约束优化问题,提出一个修正的多维滤子信赖域算法.将滤子技术引入到拟Newton信赖域方法,在每步迭代,Cauchy点用于预测有效集,此时试探步借助于求解一个较小规模的信赖域子问题获得.在一定条件下,本文所提出的修正算法对于凸约束优化问题全局收敛.数值试验验证了新算法的实际运行结果.     

求解无约束优化问题的分式模型信赖域算法

本文提出一个求解无约束优化问题的分式模型信赖域拟Newton算法.在新算法中,分式模型信赖域子问题是用简单折线法求解的.在合理假设条件下,算法的全局收敛性获得了证明.数值实验结果表明新算法是可行、有效的.     

张量方法在信赖域算法中的应用

信赖域算法是求解无约束优化问题的一种有效的算法.对于该算法的子问题,本文将原来目标函数的二次模型扩展成四次张量模型,提出了一个带信赖域约束的四次张量模型优化问题的求解算法.该方法的最大特点是:不仅在张量模型的非稳定点可以得到下降方向及相应的迭代步长,而且在非局部极小值点的稳定点也可以得到下降方向及相应的迭代步长,从而在算法产生的迭代点列中存在一个子列收敛到信赖域子问题的局部极小值点.     

一个无约束有限内存信赖域方法及其实现

本文针对大规模无约束优化问题研究了一个新的有限内存信赖域实现方法,提出了一个在有限维（维数≤2m＋1）子空间上精确求解信赖域子问题的方法,大大减少了计算量;分析了方法的收敛性,并详细给出了数值计算方法,最后通过数值实验验证了方法的有效性.     

一类带非单调线搜索的信赖域算法

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...     

解线性约束优化问题的新锥模型信赖域法

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.     

A NONMONOTONE TRUST REGION METHOD FOR NONLINEAR LEAST SQUARES PROBLEMS

In this paper we present a nonmonotone trust region method for nonlinear least squares problems with zero-residual and prove its convergence properties. The extensive numerical results are reported which show that the nonmonotone trust region method is generally superior to the usual trust region method.     

A globally convergent trust region algorithm for optimization with general constraints and simple bounds

1.IntroductionInthispaper,weconsiderthefollowingnonlinearprogr~ngproblemwherec(x)=(c,(x),c2(2),',We(.))',i(x)andci(x)(i=1,2,',m)arerealfunctions*ThisworkissupPOrtedbytheNationalNaturalScienceFOundationofChinaandtheManagement,DecisionandinformationSystemLab,theChineseAcademyofSciences.definedinD={xEReIISx5u}.Weassumethath相似文献   

A new trust region method for nonlinear equations

In this paper, a new trust region method for the system of nonlinear equations is presented in which the determining of the trust region radius incorporates the information of its natural residual. The global convergence is obtained under mild conditions. Unlike traditional trust region method, the superlinear convergence of the method is proven under the local error bound condition. This condition is weaker than the nondegeneracy assumption which is necessary for superlinear convergence of traditional trust region method. We also propose an approximate algorithm for the trust region subproblem. Preliminary numerical experiments are reported. Acknowledgements.The authors are indebted to our supervisor, Professor Y.-X. Yuan, for his excellent guidance and Jorge J. Moré for his subroutine. And we would like to thank the referees for their valuable suggestions and comments.     

A New Nonmonotonic Trust Region Algorithm for A Class of Unconstrained Nonsmooth Optimization

This paper presents a new trust region algorithm for solving a class of composite nonsmooth optimizations. It is distinguished by the fact that this method does not enforce strict monotonicity of the objective function values at successive iterates and that this method extends the existing results for this type of nonlinear optimization with smooth, or piecewise smooth, or convex objective functions or their composition. It is proved that this algorithm is globally convergent under certain conditions. Finally, some numerical results for several optimization problems are reported which show that the nonmonotonic trust region method is competitive with the usual trust region method.     

信赖域方法在Hölderian局部误差界下的收敛性质

信赖域方法是求解非线性方程组的一种重要方法.本文研究了求解非线性方程组的信赖域半径趋于零的信赖域算法在Jacobi矩阵Hölderian连续条件下的全局收敛性质,以及其在Hölderian局部误差界和Jacobi矩阵Hölderian连续条件下的收敛速度.     

Convergence Rate of The Trust Region Method for Nonlinear Equations Under Local Error Bound Condition

In this paper, we present the new trust region method for nonlinear equations with the trust region converging to zero. The new method preserves the global convergence of the traditional trust region methods in which the trust region radius will be larger than a positive constant. We study the convergence rate of the new method under the local error bound condition which is weaker than the nonsingularity. An example given by Y.X. Yuan shows that the convergence rate can not be quadratic. Finally, some numerical results are given. This work is supported by Chinese NSFC grants 10401023 and 10371076, Research Grants for Young Teachers of Shanghai Jiao Tong University, and E-Institute of Computational Sciences of Shanghai Universities. An erratum to this article is available at .     

On filter-successive linearization methods for nonlinear semidefinite programming

In this paper we present a filter-successive linearization method with trust region for solutions of nonlinear semidefinite programming. Such a method is based on the concept of filter for nonlinear programming introduced by Fletcher and Leyffer in 2002. We describe the new algorithm and prove its global convergence under weaker assumptions. Some numerical results are reported and show that the new method is potentially effcient.     

信赖域算法的修订算法

为了求得非线性优化问题的最优解,必须从收敛的可能性和收敛速度入手实现有效的计算方法.为此,通过改变作为搜索方向的下降方向,并适当修订信赖范围,在信赖域算法的基础上提出了一种修订的最优化问题的求解方法.计算方法的计算程序虽然有些复杂,但从整体收敛性和计算可行性方面来说是一个有效的方法.     

求解非线性互补问题的一个非精确信赖域方法

本文研究了基于非线性互补问题的等价非光滑优化问题的非精确依赖域方法，利用非线性规划的理论和方法，在一定条件下，获得了该方法的全局收敛性结果．