Given a single feasible solution x(F) and a single infeasible solution x(I)
of a mathematical program, we provide an upper bound to the optimal dual v
alue. We assume that x(F) satisfies a weakened form of the Slater condition
. We apply the bound to convex programs and we discuss its relation to Hoff
man-like bounds. As a special case, we recover a bound due to Mangasarian [
11] on the distance of a point to a convex set specified by inequalities.