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Zbl 0624.90062
Gill, Philip E.; Murray, Walter; Saunders, Michael A.; Tomlin, J.A.; Wright, Margaret H.
On projected Newton barrier methods for linear programming and an equivalence to Karmarkar's projective method. (English)
[J] Math. Program. 36, 183-209 (1986). ISSN 0025-5610; ISSN 1436-4646/e

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. \par 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.
[B.Strazicky]

MSC 2000:: *90C05 Linear programming
65K05 Mathematical programming (numerical methods)

Keywords: barrier function method; projected Newton search; Karamarkar's projective method

Cited in: Zbl 0944.65065 Zbl 0762.90055 Zbl 0675.90067

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