Sanjeev Arora and Satyen Kale
In Journal of the ACM, 2016. Also in proceedings of 39th ACM Symposium on Theory of Computing (STOC), 2007

Semidefinite programs (SDP) have been used in many recent approximation algorithms. We develop a general primal-dual approach to solve SDPs using a generalization of the well-known multiplicative weights update rule to symmetric matrices. For a number of problems, such as Sparsest Cut and Balanced Separator in undirected and directed weighted graphs, and the Min UnCut problem, this yields combinatorial approximation algorithms that are significantly more efficient than interior point methods. The design of our primal-dual algorithms is guided by a robust analysis of rounding algorithms used to obtain integer solutions from fractional ones.