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Equivalence of ε -Approximate Separation and Optimization in Fixed Dimensions1

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Abstract.

Given a closed, convex set X\subseteq \bbR n , containing the origin, we consider the problem (P) : max  {c^\T x\colon x ∈ X} . We show that, for a fixed dimension, n , and fixed \eps , 0 <\eps<1 , the existence of a combinatorial, strongly polynomial \eps -approximation separation algorithm for the set X is equivalent to the existence of a combinatorial, strongly polynomial \eps -approximation optimization algorithm for the problem (P) .

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Received June 5, 1996; revised September 25, 1997.

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Kabadi, S., Aneja, Y. Equivalence of ε -Approximate Separation and Optimization in Fixed Dimensions1 . Algorithmica 29, 582–594 (2001). https://doi.org/10.1007/s004530010073

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  • Key words. Strongly polynomial, Combinatorial algorithm, Convex set, Linear program.