ABSTRACT
A very challenging problem in computational optimization is the solution of models whose constraints are given by the discretization of partial differential equations. These problems are often so large that Hessian and Jacobian matrices cannot be formed or stored -- and this prevents us from applying contemporary optimization algorithms. To solve these kinds of problems, it is imperative to use multilevel techniques and matrix-free optimization methods. In this talk I will report on some recent contributions we have made in this area. Three case studies will be considered: long-range weather forecasting, model calibration in financial engineering, and a problem in cancer treatment planning.
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