Markets and the Primal-Dual Paradigm
The primal-dual paradigm was given by Kuhn in 1955. In the 1970’s and 1980’s, it yielded efficient exact algorithms for several fundamental problems in P. In the 1990’s, this paradigm yielded algorithms, with good approximation factors and good running times, for several basic NP-hard optimization problems.
Interestingly enough, over the last five years, this paradigm has yielded combinatorial algorithms for finding equilibria in several natural market models. This has involved extending the paradigm from its original setting of LP-duality to the enhanced setting of nonlinear convex programs and KKT conditions. In this talk, I will survey this new and exciting development and present some of its challenging open problems.