Before revision:  Examples comparing the cutting surface algorithm to the central cutting plane algorithm of Kortanek and No demonstrate the potential of the central cutting surface algorithm even in the solution of traditional semi-infinite convex programming problems , whose constraints are differentiable , and are indexed by an index set of low dimension.
After revision:  Examples comparing the cutting surface algorithm to the central cutting plane algorithm of Kortanek and No demonstrate the potential of our algorithm even in the solution of traditional semi-infinite convex programming problems , whose constraints are differentiable , and are indexed by an index set of low dimension.