A Trust Region Method for Optimization Problem with Singular Solutions
A Trust Region Method for Optimization Problem with Singular Solutions
复制标题
奇异解优化问题的置信域方法
DOI：
10.1007/s00245-007-9009-6
复制
发表时间：
2007
影响因子：
1.8
通讯作者：
Xiang
中科院分区：
文献类型：
--
作者：
Ju;Ling;Xiang
本文提出了一种信赖域方法，用于解处的Hessian矩阵可能为奇异的函数的最小化。在温和条件下，得到了该方法的全局收敛性。此外，我们还证明了当目标函数为islc2函数时，该方法在局部误差界条件下具有局部超线性收敛性，而不需要孤立非奇异解。这是在不假设目标函数在解处的Hessian为非奇异的情况下，第一个具有局部超线性（二次）收敛性的正则牛顿法。初步数值实验表明了该方法的有效性。
In this paper, we propose a trust region method for minimizing a function whose Hessian matrix at the solutions may be singular. The global convergence of the method is obtained under mild conditions. Moreover, we show that if the objective function isLC2function, the method possesses local superlinear convergence under the local error bound condition without the requirement of isolated nonsingular solution. This is the first regularized Newton method with trust region technique which possesses local superlinear (quadratic) convergence without the assumption that the Hessian of the objective function at the solution is nonsingular. Preliminary numerical experiments show the efficiency of the method.
DOI：
10.1023/b:coap.0000026881.96694.32
发表时间：
2004-07
影响因子：
2.2
作者：
Donghui Li;M. Fukushima;L. Qi;N. Yamashita
通讯作者：
Donghui Li;M. Fukushima;L. Qi;N. Yamashita