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Normal solutions of linear programs. (English) Zbl 0588.90058

The author introduces the definition of normal solution to a linear program, which is an exact solution with some least norm property if the linear program is solvable, otherwise an approximate solution with some least norm property also. By considering normal solutions we are led to (i) iterative successive overrelaxation (SOR) methods capable of solving very large linear programs; (ii) approximate solutions to poorly posed or unsolvable linear programs; (iii) a stable solution or approximate solution, to a linear program, endowed with a least norm property. The paper presents computational results on the comparison of one of the suggested SOR algorithms and the XMP revised simplex linear programming code (Marsten).
Reviewer: B.Strazicky

MSC:

90C06 Large-scale problems in mathematical programming
65K05 Numerical mathematical programming methods
90C05 Linear programming
90C20 Quadratic programming
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