Fisher Markets and Convex Programs

Convex programming duality is usually stated in its most general form, with convex objective functions and convex constraints. (The book by Boyd and Vandenberghe is an excellent reference [2].) At this level of generality the process of constructing a dual of a convex program is not so simple, in contrast to LP duality where there is a simple set of rules one can use for the same purpose. In this article, we consider a special class of convex programs: with convex objective functions and linear constraints, and derive a simple set of rules to construct the dual, analogous to LPs. We also show applications of this: the main application in this article will be to derive convex programs for Fisher markets.