Chapter 4 Convexity in Polynomial Optimization

Abstract

If on the one hand practice seems to reveal that convergence of the semidefinite relaxations (3.14) is often fast and even finite, on the other hand we have seen that their size grows rapidly with the rank in the hierarchy. And so, if sparsity in the original problem data is not exploited, the approach is limited to small or to medium size problems only. On the other hand, it is well known that a large class of convex optimization problems can be solved efficiently.