Moments and Positive Polynomials


Séminaire Modèles et Algorithmes Déterministes: CASC

14/11/2019 - 15:30 Tillmann Weisser (Los Alamos National Laboratory) Salle 106 - Batiment IMAG

In my research I investigate how to use moments and positive polynomials to approximate and solve problems having genuinely non-linear and non-convex features. The general strategy is to reformulate the non-linear problem as a linear problem on moments of (finite, positive) Borel measures. By conic duality these problems have a strong relation to positive polynomials. This talk will cover three different aspects of this strategy. First, I will examplarily present a reformulation for distributionally robust chance constraints in the space of measures. Then, I will discuss a method to approximate a solution in the measure space based on certificates for non-negative polynomials. Finally, I will present the Julia package MomentOpt.jl, developed to model in the space of moments and using certificate sets to approximate solutions.