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On projected Newton barrier methods for linear programming and an equivalence to Karmarkar’s projective method. (English) Zbl 0624.90062

The barrier function method is applied to linear programming problems using a projected Newton search direction for the solution of subproblems. The relationship between the presented algorithm and Karamarkar’s projective method is discussed. It turns out that if both of these methods are applied to the same problem using the same initial point, then by using special parameter values in the barrier method one can achieve that the iterates are identical.

Algorithmic details are outlined and the performance on a standard as well as a degenerate test set is summarized. Conclusions pro and contra the barrier method are also discussed.

Reviewer: B.Strazicky

MSC:
90C05Linear programming
65K05Mathematical programming (numerical methods)
Software:
LSQR; MINOS; SPARSPAK
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