Linearly constrained convex programming as unconstrained differentiable concave programming

Recently, Fang proposed approximating a linear program in Karmarkar's standard form by adding an entropic barrier function to the objective function and using a certain geometric inequality to transform the resulting problem into an unconstrained differentiable concave program. We show that, by using standard duality theory for convex programming, the results of Fang and his coworkers can be strengthened and extended to linearly constrained convex programs and more general barrier functions.This research was supported by the National Science Foundation, Grant No. CCR-91-03804.