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Zbl 0626.90056
Vanderbei, Robert J.; Meketon, Marc S.; Freedman, Barry A.
A modification of Karmarkar's linear programming algorithm. (English)
[J] Algorithmica 1, 395-407 (1986). ISSN 0178-4617; ISSN 1432-0541/e

The authors present a modification of Karmarkar's algorithm, which uses a recentered projected gradient approach thereby obviating a priori knowledge of the optimal value of the objective function. The proof of the convergence is given assuming primal and dual nondegeneracy. \par Computational comparisons between this algorithm and the revised simplex method are reported. The authors undertook a regression on the algorithm of the time (number of iterations) as a linear function of the logarithms of m and n.
[V.Mazurow]

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

Keywords: least squares; modification; Karmarkar's algorithm; projected gradient; Computational comparisons; revised simplex method

Cited in: Zbl 0724.90038 Zbl 0675.90050 Zbl 0663.90057 Zbl 0626.90052

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