Regularized Newton Methods for Convex Minimization Problems with Singular Solutions
Regularized Newton Methods for Convex Minimization Problems with Singular Solutions
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DOI：
10.1023/b:coap.0000026881.96694.32
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发表时间：
2004-07
影响因子：
2.2
通讯作者：
Donghui Li;M. Fukushima;L. Qi;N. Yamashita
中科院分区：
文献类型：
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作者：
Donghui Li;M. Fukushima;L. Qi;N. Yamashita
本文研究了正则化牛顿法最小化 Hessian 矩阵可能处处奇异的凸函数的收敛特性。我们证明，如果目标函数是 LC2，那么该方法在局部误差界限条件下具有局部二次收敛性，而不需要孤立的非奇异解。通过使用回溯线搜索，我们将不精确的正则化牛顿方法全球化。我们表明单位步长最终被接受。有限的数值实验表明了该方法的实际优势。
This paper studies convergence properties of regularized Newton methods for minimizing a convex function whose Hessian matrix may be singular everywhere. We show that if the objective function is LC2, then the methods possess local quadratic convergence under a local error bound condition without the requirement of isolated nonsingular solutions. By using a backtracking line search, we globalize an inexact regularized Newton method. We show that the unit stepsize is accepted eventually. Limited numerical experiments are presented, which show the practical advantage of the method.