Damped Newton’s method on Riemannian manifolds

被引：0
作者：
Marcio Antônio de A. Bortoloti
Teles A. Fernandes
Orizon P. Ferreira
Jinyun Yuan
机构：
[1] DCET,School of Computer Science and Technology
[2] Universidade Estadual do Sudoeste da Bahia,undefined
[3] IME,undefined
[4] Universidade Federal de Goiás,undefined
[5] Dongguan University of Technology,undefined
来源：
Journal of Global Optimization | 2020年 / 77卷
关键词：
Global Optimization; Damped Newton method; Superlinear/Quadratic Rate; Riemannian Manifold; 90C30; 49M15; 65K05;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
A damped Newton’s method to find a singularity of a vector field in Riemannian setting is presented with global convergence study. It is ensured that the sequence generated by the proposed method reduces to a sequence generated by the Riemannian version of the classical Newton’s method after a finite number of iterations, consequently its convergence rate is superlinear/quadratic. Even at an early stage of development, we can observe from numerical experiments that DNM presented promising results when compared with the well known BFGS and Trust Regions methods. Moreover, damped Newton’s method present better performance than the Newton’s method in number of iteration and computational time.
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页码：643 / 660
页数：17
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