POP carries out researches to solve hard nonconvex polynomial optimization problems in all areas of science.
Indeed the last two decades have witnessed the emergence of polynomial optimization as a new field in which powerful positivity certificates from real algebraic geometry based on sums of squares (SOS), representations of measures by their moments, and conic optimization duality, have permitted to develop an original and systematic approach to solve (at global optimality) optimization problems with polynomial (and more generally semi-algebraic) data.