Positivity and Optimization: Beyond Polynomials

摘要: The recent progress optimization theory, due to a novel synthesis of real algebraic geometry and moment problems techniques, can naturally be reduced positivity certificates for polynomial functions defined on basic semi-algebraic sets. There are however classical applied mathematics which require exact criteria non-polynomial functions, such as splines, wavelets, periodic or almost functions. While we do not lack fine analysis results referring the traditionally stated in terms Fourier-Laplace transforms type, machinery modern theory based algebra fails when this more general context. A notorious example being stability problem differential equations with delays argument. In all these cases, must complemented by approximation results. Without aiming at completeness, present chapter offers glimpse series specific problems, identifying every instance needed run robust relaxation scheme.