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On the minimum norm solution of linear programs

On the minimum norm solution of linear programs
On the minimum norm solution of linear programs
This paper describes a new technique to find the minimum norm solution of a linear program. The main idea is to reformulate this problem as an unconstrained minimization problem with a convex and smooth objective function. The minimization of this objective function can be carried out by a Newton-type method which is shown to be globally convergent. Furthermore, under certain assumptions, this Newton-type method converges in a finite number of iterations to the minimum norm solution of the underlying linear program.
linear programs, minimum norm solution, unconstrained minimization, newton method, finite termination
0022-3239
333-345
Kanzow, C.
2f350eae-ed45-4b31-a93a-d18094788839
Qi, H.
e9789eb9-c2bc-4b63-9acb-c7e753cc9a85
Qi, L.
d1312bc6-c7fc-45e0-b75d-baaf78babbc1
Kanzow, C.
2f350eae-ed45-4b31-a93a-d18094788839
Qi, H.
e9789eb9-c2bc-4b63-9acb-c7e753cc9a85
Qi, L.
d1312bc6-c7fc-45e0-b75d-baaf78babbc1

Kanzow, C., Qi, H. and Qi, L. (2003) On the minimum norm solution of linear programs. Journal of Optimization Theory and Applications, 116 (2), 333-345. (doi:10.1023/A:1022457904979).

Record type: Article

Abstract

This paper describes a new technique to find the minimum norm solution of a linear program. The main idea is to reformulate this problem as an unconstrained minimization problem with a convex and smooth objective function. The minimization of this objective function can be carried out by a Newton-type method which is shown to be globally convergent. Furthermore, under certain assumptions, this Newton-type method converges in a finite number of iterations to the minimum norm solution of the underlying linear program.

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More information

Published date: 2003
Keywords: linear programs, minimum norm solution, unconstrained minimization, newton method, finite termination
Organisations: Operational Research

Identifiers

Local EPrints ID: 29646
URI: http://eprints.soton.ac.uk/id/eprint/29646
ISSN: 0022-3239
PURE UUID: 0b9e8adf-3efd-4f81-9cc9-065a23f2191a

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Date deposited: 12 May 2006
Last modified: 16 Mar 2024 03:41

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Contributors

Author: C. Kanzow
Author: H. Qi ORCID iD
Author: L. Qi

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