Market equilibrium via a primal-dual algorithm for a convex program

Nikhil R. Devanur, Christos H. Papadimitriou, Amin Saberi, Vijay V. Vazirani

Abstract: We give the first polynomial time algorithm for exactly computing an equilibrium for the linear utilities case of the market model defined by Fisher. Our algorithm uses the primal--dual paradigm in the enhanced setting of KKT conditions and convex programs. We pinpoint the added difficulty raised by this setting and the manner in which our algorithm circumvents it.