METHODS FOR CALCULATING LP-MINIMUM NORM SOLUTIONS OF CONSISTENT LINEAR-SYSTEMS

Authors
DAX A
Citation
A. Dax, METHODS FOR CALCULATING LP-MINIMUM NORM SOLUTIONS OF CONSISTENT LINEAR-SYSTEMS, Journal of optimization theory and applications, 83(2), 1994, pp. 333-354
Citations number
26
Categorie Soggetti
Operatione Research & Management Science",Mathematics,"Operatione Research & Management Science
Journal title
Journal of optimization theory and applications → ACNP
ISSN journal
00223239
Volume
83
Issue
2
Year of publication
1994
Pages
333 - 354
Database
ISI
SICI code
0022-3239(1994)83:2<333:MFCLNS>2.0.ZU;2-J
Abstract
This paper describes, analyzes, and tests methods for solving l(p)-min imum norm problems of the form min parallel-to X parallel-to p(p)/p, s .t. Ax = b, where 1 < p < infinity and Ax = b is a consistent system o f linear equations. The paper presents a primal Newton method for prob lems with p > 2 and a dual Newton method that is suitable when 1 < p < 2. Primal-dual methods are also introduced. Numerical experiments ill ustrate the usefulness of the proposed methods.