Hostname: page-component-848d4c4894-ndmmz Total loading time: 0 Render date: 2024-05-08T20:00:02.452Z Has data issue: false hasContentIssue false
  • English
  • Français

An algorithm for solving the restricted least squares problem

Published online by Cambridge University Press:  17 February 2009

David Clark
David Clark
Affiliation:
Computing Research Group, Australian National University, Canberra, A.C.T. 2600
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

This paper presents an algorithm to solve the least squares problem when the parameters are restricted to be non-negative. The algorithm is based on the branch and bound method which has been suggested for this problem, and shares with it the property that an unrestricted least squares subproblem is solved at each step. However, improvements have been made to the branching rules by making use of the convexity of the problem, and the Kuhn–Tucker conditions are used to test for optimality. The resulting algorithm becomes essentially iterative in nature, and linearity of the number of subproblems solved can be shown under assumptions which have always been observed in practice.

Type
Research Article
Information
The ANZIAM Journal , Volume 21 , Issue 3 , January 1980 , pp. 345 - 356
Copyright
Copyright © Australian Mathematical Society 1980

References

[1]Armstrong, R. D. and Frome, E. L., “A branch-and-bound solution of a restricted least squares problem”, Technometrics 18 (1976), 447–450.CrossRefGoogle Scholar
[2]Beale, E. M. L., “Selecting an optimum subset”, Chapter 22 of Integer and non-linear programming (ed. Abadje, J.) (Amsterdam: North Holland Publishing Co., 1970).Google Scholar
[3]Judge, G. G. and Takayama, T., “Inequality restrictions in regression analysis”, J. Amer. Statist. Assoc. 61 (1966), 166–181.CrossRefGoogle Scholar
[4]Waterman, M. S., “A restricted least squares problem”, Technometrics 16 (1974), 135–136.CrossRefGoogle Scholar