14/11/2019 - 15:30 Tillmann Weisser (Los Alamos National Laboratory)
In my research I investigate how to use moments and positive polynomialsto approximate and solve problems having genuinely non-linear and non-convexfeatures. The general strategy is to reformulate the non-linear problem as alinear problem on moments of (finite, positive) Borel measures. By conic dualitythese problems have a strong relation to positive polynomials. This talk willcover three different aspects of this strategy. First, I will examplarily presenta reformulation for distributionally robust chance constraints in the space ofmeasures. Then, I will discuss a method to approximate a solution in themeasure space based on certificates for non-negative polynomials. Finally, I willpresent the Julia package MomentOpt.jl, developed to model in the space ofmoments and using certificate sets to approximate solutions.