A toolbox for fast and approximate solutions for large linear and semidefinite programs

Abstract

The multiplicative weights update is an algorithmic design technique that, over the years, has been discovered independently by several groups of researchers in different contexts. The earliest known use of this technique is by Brown and vonNeumann for the computation of equilibrium strategies in zero-sum games. These ideas and variants thereof have found applications in solving games, linear and semidefinite programming, computational geometry, machine learning, auctions and mechanism design, as well as data privacy.In this paper, we focus on the use of this technique for solving zero-sum games, and for solving linear and semidefinite programs. In particular, we present empirical results on the efficacy of this method to solve linear and semidefinite programs approximately.Our results suggest that this could be the preferred method in scenarios where one is interested in obtaining reasonably good results very quickly, as well as in scenarios where the problem sizes are very large. Another advantage of this technique is that it is amenable to a parallel or distributed implementation unlike interior-point or simplex methods, and therefore could form a primitive in cluster computing, or in sensor networks.