Abstract
The ellipsoid method finds an optimal solution (if one exists) of a linear programming problem. Khachiyan showed that the running time of the algorithm is bounded from above by a fixed polynomial in the size of the data. From a theoretical point of view this result was very important. However, the bound did not guarantee good performances in practice. Yamnitsky and Levin (1982) proposed a variant using simplices instead of ellipsoids. In this paper we investigate a variant of the ellipsoid method due to Prakash and Supowit (1991), which we call the simplices method. This paper works out the details of the theory and presents the numerical results of an implementation of the method. The results suggest that in practice the number of iterations used by it may be considerably less than that of the ellipsoid method.
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© 1996 Springer-Verlag Berlin Heidelberg
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Faigle, U., Hunting, M., Kern, W. (1996). On a Variant of the Ellipsoid Method: Using Simplices instead of Ellipsoids. In: Kleinschmidt, P., Bachem, A., Derigs, U., Fischer, D., Leopold-Wildburger, U., Möhring, R. (eds) Operations Research Proceedings 1995. Operations Research Proceedings, vol 1995. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-80117-4_1
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DOI: https://doi.org/10.1007/978-3-642-80117-4_1
Publisher Name: Springer, Berlin, Heidelberg
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