Applied & Computational Mathematics Seminar: Global minimization of integral functionals via polynomial optimization

Speaker:  Giovanni Fantuzzi, Imperial College, London

Title:  Global minimization of integral functionals via polynomial optimization

Abstract:   

The problem of minimizing an integral functional over all functions satisfying a given set of constraints is central to many disciplines, including material science, fluid mechanics and pattern formation. When the functional to be minimized is nonconvex or the imposed constraints are nonlinear, traditional computational techniques are very effective in finding local minimizers, but it is usually almost impossible to check if a local minimizer is also a global one. In this talk I will describe how tools for polynomial optimization, emerged in the early 2000s, can be used to certify the global optimality of known local minimizers to an integral functional. I will then show how the same polynomial optimization tools can be combined with finite-element discretizations in order to devise numerical schemes that, under suitable conditions, provably converge to a global minimizer of an integral functional. The potential and current limitations of these approaches will be illustrated on a series of examples.

Time:   Friday, November 5, 2021, 1:30pm – 2:30pm

Place:  Zoom - https://gmu.zoom.us/j/96953045320