Abstract
The non-differentiable L 1 function is approximated by the Huber function, such that the original L 1 estimation problem is transformed to a sequence of unconstrained minimization problems. An algorithm is considered for the Huber problem. Numerical experiments are reported and comparisons within different methods are made.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
D.F. Andrews, PJ. Bickel, F.R. Hampel, P.J. Huber, W.H. Rogers, J.W. Tukey, Robust Estimates of Location, Princeton University Press, Princeton, NJ, 1972.
R. Fletcher, Practical Methods of Optimization, Vol. I: Unconstained Optimization, John Wiley and Sons, Chichester, 1980.
L. Gao, A Method of Continuous Optimization for Nonlinear L1 norm Problem, to appear.
L. Gao and K. Madsen, Robust Nonlinear Data Fitting, In Numerical Analysis 1987, D. f. Griffiths and G.A. Watson, eds., Pitman Research Notes in Mathematics Series 170, Longman, UK, pp 176–191, 1988
H. Ekblom, L. Gao and K. Madsen, Algorithms for Non-linear Huber Regression with Variable Scale, Technical University of Denmark, Report NI90-10, 1990
J. Hald and K. Madsen, Combined LP and Quasi-Newton methods for Nolinear L1Optimization, SIAM J. Numer. Anal, Vol. 20, pp. 68–80, 1985
P. Huber, Robust Statistics, John Wiley, New York, 1986.
K. Madsen and O. Tingleff, Robust Subroutines for Nonlinear Optimization, Technical University of Denmark, Report NI-90-06, 1990
D. Marquardt, An Algorithm for Least Squares Estimation of Nonlinear Parameters, SIAM J. Math. 11, pp. 431–441, 1963
M.R. Osborne, Some Espect of Nonlinear Least Squares Calculations, in Numerical Methods for Nonlinear Optimization, (Ed. F.Lootsma ). Academic Press, New York and London, 1972
A. Tishler and I. Zang, An Absolute Deviations Curve-Fitting Algorithm for Nonlinear Models, TIMS Studies in the Management Sciences 19, pp 81–103, 1982
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1998 Kluwer Academic Publishers
About this chapter
Cite this chapter
Gao, L. (1998). Using Huber Method to Solve Nonlinear L 1-Norm Problem. In: Yuan, Yx. (eds) Advances in Nonlinear Programming. Applied Optimization, vol 14. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-3335-7_12
Download citation
DOI: https://doi.org/10.1007/978-1-4613-3335-7_12
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4613-3337-1
Online ISBN: 978-1-4613-3335-7
eBook Packages: Springer Book Archive