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

• Main Authors: Castelani, E. V, Lopes, R, Shirabayashi, W. V. I, Sobral, F. N. C
• Format: Journal Article
• Language: English
• Published: 29-11-2019
• Subjects: Computer Science - Learning; Mathematics - Optimization and Control
• DOI: 10.48550/arxiv.1911.13078

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.