Computing approximately optimal solutions is an attractive way to cope with NP-hard optimization problems. In the past decade or so, semidefinite programming or SDP (a form of convex optimization that generalizes linear programming) has emerged as a powerful tool for designing such algorithms, and the last few years have seen a profusion of results (worst-case algorithms, average case algorithms, impossibility results, etc).

This talk will be a survey of this area and these recent results. We will see that analysing semidefinite program draws upon ideas from a variety of other areas, and has also led to new results in mathematics. At the end we will touch upon work that greatly improves the running time of SDP-based algorithms, making them potentially quite practical.

The survey will be essentially self-contained.

Sanjeev Arora is Professor of Computer Science at Princeton University and works in computational complexity theory, approximation algorithms for NP-hard problems, geometric algorithms, and probabilistic algorithms. He has received the ACM Doctoral Dissertation Award, the SIGACT-EATCS Goedel Prize, and the Packard Fellowship.