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On the minimum norm solution of linear programs. (English) Zbl 1043.90046
Summary: 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.

MSC:
90C05 Linear programming
90C53 Methods of quasi-Newton type
90C20 Quadratic programming
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