Table of Contents
ISRN Operations Research
Volume 2013, Article ID 393482, 7 pages
Research Article

A Spline Smoothing Newton Method for Distance Regression with Bound Constraints

Li Dong1,2 and Bo Yu1

1School of Mathematical Sciences, Dalian University of Technology, Dalian, Liaoning 116024, China
2College of Science, Dalian Nationalities University, Dalian, Liaoning 116605, China

Received 15 February 2013; Accepted 19 March 2013

Academic Editors: I. Ahmad and X.-M. Yuan

Copyright © 2013 Li Dong and Bo Yu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Orthogonal distance regression is arguably the most common criterion for fitting a model to data with errors in the observations. It is not appropriate to force the distances to be orthogonal, when angular information is available about the measured data points. We consider here a natural generalization of a particular formulation of that problem which involves the replacement of norm by norm. This criterion may be a more appropriate one in the context of accept/reject decisions for manufacture parts. For distance regression with bound constraints, we give a smoothing Newton method which uses cubic spline and aggregate function, to smooth max function. The main spline smoothing technique uses a smooth cubic spline instead of max function and only few components in the max function are computed; hence it acts also as an active set technique, so it is more efficient for the problem with large amounts of measured data. Numerical tests in comparison to some other methods show that the new method is very efficient.