2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/210664We prove an upper bound on the degree complexity of Putinar's Positivstellensatz. This bound is much worse than the one obtained previously for Schmüdgen's Positivstellensatz but it depends on the same parameters. As a consequence, we get information about the convergence rate of Lasserre's procedure for optimization of a polynomial subject to polynomial constraints.Algebraic GeometryCommutative AlgebraOptimization and Control11E25, 13J30, 14P10, 44A60, 68W40, 90C22text