Given a closed, convex set X\subseteq \bbR
n
, containing the origin, we consider the problem (P) : max {cˆ 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) .
