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A modification of Karmarkar’s linear programming algorithm. (English) Zbl 0626.90056

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.

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.

Reviewer: V.Mazurow

MSC:
90C05Linear programming
65K05Mathematical programming (numerical methods)
References:
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[6]N. Karmarkar, A new polynomial-time algorithm for linear programming,Combinatorica,4 (1984), 373–395. · Zbl 0557.90065 · doi:10.1007/BF02579150
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[10]J. A. Tomlin, An experimental approach to Karmarkar’s projective method for linear programming, Manuscript, Ketron Inc., Mountain View, CA, 1985.