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Center for Nonlinear Studies |
Nonlinearities are the source of difficulty in many mathematical formulations of problems from all natural science. In order to simulate such problems computationally the nonlinearities are often neglected even if this implies a less accurate representation of the natural phenomena.One of my research lines is to use the theory of measures and moments to lift nonlinear problems in a space, where they become linear without anyinformation loss. Under certain conditions the lifted problems are computationally tractable through characterizations of positive polynomials (which is my second line of research). In this talk I am going to present the framework of the Generalized Moment Problem and how to approximate solutions with Positive Polynomials. In the second part I will illustrate the diversity of thisstrategy on examples from Global Optimization, approximation of Chance Constraints and numerically solving Hyperbolic Conservation Laws.
Host: David Métivier