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
333-345
Kanzow, C.
2f350eae-ed45-4b31-a93a-d18094788839
Qi, H.
e9789eb9-c2bc-4b63-9acb-c7e753cc9a85
Qi, L.
d1312bc6-c7fc-45e0-b75d-baaf78babbc1
2003
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), .
(doi:10.1023/A:1022457904979).
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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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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Author:
C. Kanzow
Author:
L. Qi
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