A recursive algorithm for nonlinear least-squares problems

被引：0

作者：

A. Alessandri

M. Cuneo

S. Pagnan

M. Sanguineti

机构：

[1] University of Genoa,Department of Production Engineering, Thermoenergetics, and Mathematical Models (DIPTEM)

[2] ISSIA-CNR National Research Council of Italy,Institute of Intelligent Systems for Automation

[3] University of Genoa,Department of Communications, Computer and System Sciences (DIST)

来源：

Computational Optimization and Applications | 2007年 / 38卷

关键词：

Nonlinear programming; Nonlinear least squares; Extended Kalman filter; Recursive optimization; Batch algorithms;

D O I：

暂无

中图分类号：

学科分类号：

摘要：

The solution of nonlinear least-squares problems is investigated. The asymptotic behavior is studied and conditions for convergence are derived. To deal with such problems in a recursive and efficient way, it is proposed an algorithm that is based on a modified extended Kalman filter (MEKF). The error of the MEKF algorithm is proved to be exponentially bounded. Batch and iterated versions of the algorithm are given, too. As an application, the algorithm is used to optimize the parameters in certain nonlinear input–output mappings. Simulation results on interpolation of real data and prediction of chaotic time series are shown.

引用

页码：195 / 216

页数：21

共 50 条

[11] Nonlinear least-squares estimation [J].

Pollard, D ;

Radchenko, P .

JOURNAL OF MULTIVARIATE ANALYSIS, 2006, 97 (02) :548-562

[12] A BRIEF SURVEY OF METHODS FOR SOLVING NONLINEAR LEAST-SQUARES PROBLEMS [J].

Mohammad, Hassan ;

Waziri, Mohammed Yusuf ;

Santos, Sandra Augusta .

NUMERICAL ALGEBRA CONTROL AND OPTIMIZATION, 2019, 9 (01) :1-13

[13] CONVERGENCE OF A REGULARIZED EUCLIDEAN RESIDUAL ALGORITHM FOR NONLINEAR LEAST-SQUARES [J].

Bellavia, S. ;

Cartis, C. ;

Gould, N. I. M. ;

Morini, B. ;

Toint, Ph. L. .

SIAM JOURNAL ON NUMERICAL ANALYSIS, 2010, 48 (01) :1-29

[14] A NONMONOTONE MATRIX-FREE ALGORITHM FOR NONLINEAR EQUALITY-CONSTRAINED LEAST-SQUARES PROBLEMS [J].

Bergou, El Houcine ;

Diouane, Youssef ;

Kungurtsev, Vyacheslav ;

Royer, Clement W. .

SIAM JOURNAL ON SCIENTIFIC COMPUTING, 2021, 43 (05) :S743-S766

[15] A SPECIAL NONLINEAR LEAST-SQUARES PROBLEM [J].

SCITOVSKI, R .

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 1994, 53 (03) :323-331

[16] ON THE USE OF PRODUCT STRUCTURE IN SECANT METHODS FOR NONLINEAR LEAST-SQUARES PROBLEMS [J].

HUSCHENS, J .

SIAM JOURNAL ON OPTIMIZATION, 1994, 4 (01) :108-129

[17] Stable factorized quasi-Newton methods for nonlinear least-squares problems [J].

Ma, XF ;

Fung, R ;

Ying, K ;

Xu, CX .

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2001, 129 (1-2) :1-14

[18] Regularization Methods for Uniformly Rank-Deficient Nonlinear Least-Squares Problems [J].

J. Eriksson ;

P. A. Wedin ;

M. E. Gulliksson ;

I. Söderkvist .

Journal of Optimization Theory and Applications, 2005, 127 :1-26

[19] Alternative structured spectral gradient algorithms for solving nonlinear least-squares problems [J].

Yahaya, Mahmoud Muhammad ;

Kumam, Poom ;

Awwal, Aliyu Muhammed ;

Aji, Sani .

HELIYON, 2021, 7 (07)

[20] Algorithm 768: TENSOLVE: A software package for solving systems of nonlinear equations and nonlinear least-squares problems using tensor methods [J].

Bouaricha, A ;

Schnabel, RB .

ACM TRANSACTIONS ON MATHEMATICAL SOFTWARE, 1997, 23 (02) :174-195

← 1 2 3 4 5 →