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广义拟牛顿算法对一般目标函数的收敛性 总被引:2,自引:0,他引:2
本文证明了求解无约束最优化的广义拟牛顿算法在Goldstein非精确线搜索下对一般目标函数的全局收敛性,并在一定条件下证明了算法的局部超线性收敛性。 相似文献
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《数学的实践与认识》2017,(19)
为了求解Hilbert空间中算子方程或minimax问题,构造了一类无穷维空间中的不精确拟牛顿算法,并考虑了其线性收敛性和超线性收敛性,是对有限维空间中不精确拟牛顿法的推广.当迭代算子由Broyden修正给出时,在一定的假设条件下,得到了不精确Broyden方法的线性收敛性和超线性收敛性.这为使用不精确拟牛顿法结合投影法求解算子方程做好了准备. 相似文献
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本文提供了在没有非奇异假设的条件下,求解有界约束半光滑方程组的投影信赖域算法.基于一个正则化子问题,求得类牛顿步,进而求得投影牛顿步.在合理的假设条件下,证明了算法不仅具有整体收敛性而且保持超线性收敛速率. 相似文献
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提出了结合Lanczos分解技术不精确Newton法求解有界变量约束非线性系统.通过Lanczos分解技术解一个仿射二次模型获得迭代方向.利用内点回代线搜索技术,沿着这个方向得到一个可接受的步长.在合理的假设条件下,证明了算法的整体收敛性与局部超线性收敛速率.此外,数值结果表明了算法的有效性. 相似文献
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在凸规划理论中,通过KT条件,往往将约束最优化问题归结为一个混合互补问题来求解。该文就正则解和一般解两种情形分别给出了求解混合互补问题牛顿型算法的二阶收敛性的充分性条件,并在一定条件下证明了非精确牛顿法和离散牛顿法所具有的二阶收敛性。 相似文献
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《数学物理学报(A辑)》2015,(4)
基于一个光滑函数,就单调对称锥互补问题,给出了一种解决高维对称锥互补问题的非精确光滑牛顿算法.在适当条件下,证明了该算法具有全局收敛性和局部二次收敛性.数值试验证实了算法对大规模对称锥互补问题的可行性和有效性. 相似文献
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一类广义拟牛顿算法的收敛性 总被引:2,自引:0,他引:2
本文提出一类广义拟牛顿算法,新类算法降低了关于目标函数的假设条件,将线搜索扩展 到一般形式,它概括了若干种常用的非精确线搜索技术.此外,算法对迭代校正公式中的参数Φk的 选取范围做了较大扩展(可以取负值). 相似文献
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The Inexact Newton-Like Method for Inverse Eigenvalue Problem 总被引:1,自引:0,他引:1
In this paper, we consider using the inexact Newton-like method for solving inverse eigenvalue problem. This method can minimize the oversolving problem of Newton-like methods and hence improve the efficiency. We give the convergence analysis of the method, and provide numerical tests to illustrate the improvement over Newton-like methods. 相似文献
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T. J. Ypma 《Numerische Mathematik》1984,45(2):241-251
Summary Newton-like methods in which the intermediate systems of linear equations are solved by iterative techniques are examined. By applying the theory of inexact Newton methods radius of convergence and rate of convergence results are easily obtained. The analysis is carried out in affine invariant terms. The results are applicable to cases where the underlying Newton-like method is, for example, a difference Newton-like or update-Newton method. 相似文献
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Convergence behaviour of inexact Newton methods 总被引:5,自引:0,他引:5
Benedetta Morini. 《Mathematics of Computation》1999,68(228):1605-1613
In this paper we investigate local convergence properties of inexact Newton and Newton-like methods for systems of nonlinear equations. Processes with modified relative residual control are considered, and new sufficient conditions for linear convergence in an arbitrary vector norm are provided. For a special case the results are affine invariant.
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《Journal of Computational and Applied Mathematics》2006,191(1):143-164
Under weak Lipschitz condition, local convergence properties of inexact Newton methods and Newton-like methods for systems of nonlinear equations are established in an arbitrary vector norm. Processes with modified relative residual control are considered; the results easily provide an estimate of convergence ball for inexact methods. For a special case, the results are affine invariant. Some applications are given. 相似文献
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In this paper, a new line search filter algorithm for equality constrained optimization is presented. The approach belongs to the class of inexact Newton-like methods. It can also be regarded as an inexact version of generic sequential quadratic programming (SQP) methods. The trial step is obtained by truncatedly solving the primal-dual system based on any robust and efficient linear system solver. Practical termination tests for the linear system solver are established to ensure global convergence. Preliminary numerical results demonstrate the approach is potentially useful. 相似文献
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We present a local convergence analysis of inexact Newton-like methods for solving nonlinear equations under majorant conditions.
This analysis provides an estimate of the convergence radius and a clear relationship between the majorant function, which
relaxes the Lipschitz continuity of the derivative, and the nonlinear operator under consideration. It also allow us to obtain
some important special cases. 相似文献
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Ioannis K. Argyros 《Journal of Applied Mathematics and Computing》1999,6(2):291-304
Affine invariant sufficient conditions are given for two local convergence theorems involving inexact Newton-like methods. The first uses conditions on the first Fréchet-derivative whereas the second theorem employs hypotheses on the second. Radius of convergence as well as rate of convergence results are derived. Results involving superlinear convergence and known to be true for inexact Newton methods are extended here. Moreover, we show that under hypotheses on the second Fréchet-derivative our radius of convergence is larger than the corresponding one in [10]. This allows a wider choice for the initial guess. A numerical example is also provided to show that our radius of convergence is larger than the one in [10]. 相似文献
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In this paper, we consider inexact Newton and Newton-like methods andprovide new convergence conditions relating the forcing terms to theconditioning of the iteration matrices. These results can be exploited wheninexact methods with iterative linear solvers are used. In this framework,preconditioning techniques can be used to improve the performance ofiterative linear solvers and to avoid the need of excessively small forcingterms. Numerical experiments validating the theoretical results arediscussed. 相似文献
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We propose a Ulm-like method for solving inverse eigenvalue problems, which avoids solving approximate Jacobian equations comparing with other known methods. A convergence analysis of this method is provided and the R-quadratic convergence property is proved under the assumption of the distinction of given eigenvalues. Numerical experiments as well as the comparison with the inexact Newton-like method are given in the last section. 相似文献
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Fang Lu 《Applicable analysis》2013,92(8):1567-1586
In the context of Euclidean spaces, we present an extension of the Newton-like method for solving vector optimization problems, with respect to the partial orders induced by a pointed, closed and convex cone with a nonempty interior. We study both exact and inexact versions of the Newton-like method. Under reasonable hypotheses, we prove stationarity of accumulation points of the sequences produced by Newton-like methods. Moreover, assuming strict cone-convexity of the objective map to the vector optimization problem, we establish convergence of the sequences to an efficient point whenever the initial point is in a compact level set. 相似文献