A new MM algorithm for root-finding problems

Li, Xun-Jian1; Li, Shuang2; Tian, Guo-Liang3

2024-06-01

10.1111/stan.12345

STATISTICA NEERLANDICA   影响因子和分区

0039-0402

1467-9574

The minorization-maximization (MM) algorithm is an optimization technique for iteratively calculating the maximizer of a concave target function rather than a root-finding tool. In this paper, we in the first time develop the MM algorithm as a new method for seeking the root x* of a univariate nonlinear equation g(x) = 0. The key idea is to transfer the root-finding issue to iteratively calculate the maximizer of a concave target function by designing a new MM algorithm. According to the ascent property of the MM algorithm, we know that the proposed algorithm converges to the root x* and does not depend on any initial values, in contrast to Newton's method. Several statistical examples are provided to demonstrate the proposed algorithm.

integral version of Taylor expansion MM algorithm Newton's method optimization univariate nonlinear equation

SCI

英语

通讯

Mathematics

Statistics & Probability

WOS:001237929000001

WILEY

MATHEMATICS

Web of Science

1.Hong Kong Polytech Univ, Dept Appl Math, Hong Kong, Peoples R China
2.Southern Univ Sci & Technol, Dept Math, Shenzhen, Peoples R China
3.Southern Univ Sci & Technol, Dept Stat & Data Sci, Shenzhen 518055, Guangdong, Peoples R China

Li, Xun-Jian,Li, Shuang,Tian, Guo-Liang. A new MM algorithm for root-finding problems[J]. STATISTICA NEERLANDICA,2024.

Li, Xun-Jian,Li, Shuang,&Tian, Guo-Liang.(2024).A new MM algorithm for root-finding problems.STATISTICA NEERLANDICA.

Li, Xun-Jian,et al."A new MM algorithm for root-finding problems".STATISTICA NEERLANDICA (2024).