On the Lasserre hierarchy of semidefinite programming relaxations of convex polynomial optimization problems

The Lasserre hierarchy of semidefinite programming approximations to convex polynomial optimization problems is known to converge finitely under some assumptions. [J. B. Lasserre, Convexity in semialgebraic geometry and polynomial optimization, SIAM J. Optim., 19 (2009), pp. 1995–2014]. We give a new proof of the finite convergence property under weaker assumptions than were known before. In addition, we show that—under the assumptions for finite convergence—the number of steps needed for convergence depends on more than the input size of the problem.