Convergence and Complexity Analysis of a Levenberg-Marquardt Algorithm for Inverse Problems

被引：57

作者：

Bergou, El Houcine ^{[1
,2
]}

Diouane, Youssef ^{[3
]}

Kungurtsev, Vyacheslav ^{[4
]}

机构：

[1] Univ Paris Saclay, MaIAGE, INRAE, F-78350 Jouy En Josas, France

[2] KAUST, Thuwal, Saudi Arabia

[3] Univ Toulouse, ISAE SUPAERO, F-31055 Toulouse 4, France

[4] Czech Tech Univ, Fac Elect Engn, Dept Comp Sci, Prague, Czech Republic

来源：

JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS | 2020年 / 185卷 / 03期

关键词：

Inverse problems; Levenberg-Marquardt method; Worst-case complexity bound; Global and local convergence; EQUATIONS;

D O I：

10.1007/s10957-020-01666-1

中图分类号：

C93 [管理学]; O22 [运筹学];

学科分类号：

070105 ; 12 ; 1201 ; 1202 ; 120202 ;

摘要：

The Levenberg-Marquardt algorithm is one of the most popular algorithms for finding the solution of nonlinear least squares problems. Across different modified variations of the basic procedure, the algorithm enjoys global convergence, a competitive worst-case iteration complexity rate, and a guaranteed rate of local convergence for both zero and nonzero small residual problems, under suitable assumptions. We introduce a novel Levenberg-Marquardt method that matches, simultaneously, the state of the art in all of these convergence properties with a single seamless algorithm. Numerical experiments confirm the theoretical behavior of our proposed algorithm.

引用

页码：927 / 944

页数：18

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