A pathological semi-infinite program verifying Karlovitz's conjecture

In 1965, Duffin and Karlovitz approximated semi-infinite linear programs by a sequence of linear programs where thenth approximating program minimizes the objective function, subject to the firstn constraints. At that time, Karlovitz conjectured the existence of a semi-infinite convex program without a duality gap, whose approximating programs have a duality gap. The purpose of this note is to provide such an example.The author completed this work while at the University of Illinois at Urbana-Champaign, Illinois.