Probabilistic bounds on one step objective/potential function improvement in Karmarkar's algorithm
RAIRO - Operations Research - Recherche Opérationnelle, Tome 28 (1994) no. 4, pp. 329-355.
@article{RO_1994__28_4_329_0,
     author = {Minoux, M.},
     title = {Probabilistic bounds on one step objective/potential function improvement in {Karmarkar's} algorithm},
     journal = {RAIRO - Operations Research - Recherche Op\'erationnelle},
     pages = {329--355},
     publisher = {EDP-Sciences},
     volume = {28},
     number = {4},
     year = {1994},
     mrnumber = {1304247},
     zbl = {0857.90084},
     language = {en},
     url = {http://www.numdam.org/item/RO_1994__28_4_329_0/}
}
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Minoux, M. Probabilistic bounds on one step objective/potential function improvement in Karmarkar's algorithm. RAIRO - Operations Research - Recherche Opérationnelle, Tome 28 (1994) no. 4, pp. 329-355. http://www.numdam.org/item/RO_1994__28_4_329_0/

1. I. Adler, N. Karmarkar, M. G. C. Resende and G. Veiga, An implementation of Karmarkar's algorithm for linear programming, Dept. Industrial Engineering and Operations Research, University of California, Berkeley, 1988. | Zbl

2. K. M. Anstreicher, The worst-case step in Karmarkar's algorithm, Mathematics of Ops. Res., 1989, 14, 2, pp. 294-302. | MR | Zbl

3. C. Mc Diarmid, On the improvement per iteration in Karmarkar's method for linear programming, Institute of Economics and Statistics, Oxford University, England, 1986.

4. R. B. Goldstein, Chi-square quantiles, Communications of the A. C. M., 1973, 6, n° 8, pp. 483-485.

5. N. Karmarkar, A new polynomial-time algorithm for linear programming, Combinatorica, 1984, 4, 4, pp. 373-395. | MR | Zbl

6. M. Minoux, Towards a probabilistic analysis of Karmarkar's algorithm, Colloque Franco-Soviétique de Programmation Mathématique. Marseille, Luminy 8-12 Octobre 1990.

7. A. S. Nemirovski, An algorithm of the Karmarkar type, Tekhnicheskaya Kibernetika n°1, 1987, p. 105-118, English Translation in Scripta Technica 1988. | MR | Zbl

8. M. Padberg, A different convergence proof of the projective method for linear programming, New York University, 1985. | MR | Zbl

9. M. J. D. Powell, On the number of iterations of Karmarkar's algorithm for linear programming, Mathematical Programming, 1993, 62, pp. 153-197. | MR | Zbl

10. J. A. Tomlin, An experimental approach to Karmarkar's projective method for linear programming, Ketron, Inc., Mountain View, CA 94040, 1985. | Zbl

11. M. J. Todd, Anticipated behaviour of Karmarkar's algorithm, Technical Report n° 879, Cornell University, Ithaca, New York, 14853, 1989.