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Mathematics Colloquium: Quasi-variational inequalities in function spaces: Applications, theory and solution algorithms

Speaker: Carlos Rautenberg, George Mason University

Title: Quasi-variational inequalities in function spaces: Applications, theory and solution algorithms

Abstract: Quasi-variational inequalities (QVIs) were introduced by Bensoussan and Lions in the 1970’s, and are generalizations of variational inequalities (VIs) where the associated constraint set is not known a priori. In general, QVIs arise in many applications involving partial differential operators and where very nonlinear, nonconvex and nonsmooth phenomena lead to state-dependent constraints. The fields where QVI formulations are prevalent involve game theory, continuum mechanics, and electromagnetism, among others. Fundamental difficulties here are of analytical as well as of numerical nature: For example, QVIs are not first order optimality conditions of any optimization problem and hence direct methods of calculus of variations are not applicable. In this talk, we consider state of the art methods to deal with existence and approximation of solutions to QVIs with obstacle and gradient type constraints. We further provide stability results for the solution set in cases where multiple solutions are present and study novel optimal control problems with QVIs as constraints. Finally, we present numerical tests for elliptic and parabolic problems involving a variety of applications.

Time: Friday, October 4, 2019, 3:30-4:20 p.m.

Place: Exploratory Hall, room 4106

Refreshments will be served at 3:00 p.m.