Moments and Positive Polynomials

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.