DMCA
Double Description Method Revisited (1996)
| Citations: | 108 - 2 self |
BibTeX
@MISC{Fukuda96doubledescription,
author = {Komei Fukuda and Alain Prodon},
title = {Double Description Method Revisited},
year = {1996}
}
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Abstract
. The double description method is a simple and useful algorithm for enumerating all extreme rays of a general polyhedral cone in IR d , despite the fact that we can hardly state any interesting theorems on its time and space complexities. In this paper, we reinvestigate this method, introduce some new ideas for efficient implementations, and show some empirical results indicating its practicality in solving highly degenerate problems. 1 Introduction A pair (A; R) of real matrices A and R is said to be a double description pair or simply a DD pair if the relationship Ax 0 if and only if x = R for some 0 holds. Clearly, for a pair (A; R) to be a DD pair, it is necessary that the column size of A is equal to the row size of R, say d. The term "double description" was introduced by Motzkin et al. [MRTT53], and it is quite natural in the sense that such a pair contains two different descriptions of the same object. Namely, the set P (A) represented by A as P (A) = fx 2 IR d : Ax...
Keyphrases
double description method dd pair relationship ax double description pair general polyhedral cone empirical result new idea degenerate problem column size interesting theorem different description introduction pair extreme ray row size term double description efficient implementation space complexity real matrix useful algorithm
