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A robust method based on LOVO functions for solving least squares problems

E. V. Castelani(evcastelani***at***uem.br)
R. Lopes(ronaldo_lps***at***hotmail.com)
W. V. I. Shirabayashi(wvishirabayashi***at***uem.br)
F. N. C. Sobral(fncsobral***at***uem.br)

Abstract: The robust adjustment of nonlinear models to data is considered in this paper. When data comes from real experiments, it is possible that measurement errors cause the appearance of discrepant values, which should be ignored when adjusting models to them. This work presents a Lower Order-value Optimization (LOVO) version of the Levenberg-Marquardt algorithm, which is well suited to deal with outliers in fitting problems. A general algorithm is presented and convergence to stationary points is demonstrated. Numerical results show that the algorithm is successfully able to detect and ignore outliers without too many specific parameters. Parallel and distributed executions of the algorithm are also possible, allowing for the use of larger datasets. Comparison against publicly available robust algorithms shows that the present approach is able to find better adjustments in well known statistical models.

Keywords: Lower Order-Value Optimization, Levenberg-Marquardt, Outlier Detection, Robust Least Squares

Category 1: Nonlinear Optimization (Nonlinear Systems and Least-Squares )

Category 2: Convex and Nonsmooth Optimization (Nonsmooth Optimization )

Category 3: Optimization Software and Modeling Systems (Parallel Algorithms )

Citation: Department of Mathematics, State University of Maringá, Maringá, Paraná, Brazil. November 2019.

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Entry Submitted: 11/29/2019
Entry Accepted: 11/29/2019
Entry Last Modified: 11/29/2019

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