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On the Minimum Norm Solution of Linear Programs |
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| Authors: | C Kanzow H Qi L Qi |
| Institution: | (1) Institute of Applied Mathematics and Statistics, University of Würzburg, Am Hubland, Würzburg, Germany;(2) Department of Applied Mathematics, Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong;(3) Department of Applied Mathematics, Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong |
| 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. |
| Keywords: | Linear programs minimum norm solution unconstrained minimization Newton method finite termination |
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