IMath Seminar (Feb 24): Dr. John Sebastian Simon

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You are all invited to a seminar featuring:
Dr. John Sebastian Simon, Johann Radon Institute for Computation and Applied Mathematics, Austria (hosted by the ModApp Group)

Talk:Shape optimization in the presence of missing Dirichlet data

This is an in-person event and it will be held on Monday, February 24, 2025, 11:00 AM at the Conference room. 

Abstract:

In this talk, we consider a shape optimization problem governed by an elliptic equation, where the Dirichlet boundary condition includes missing data. The problem is formulated as an optimization over the deformation field, which modifies the spatial domain in which the Poisson equation is posed. To address the missing boundary data, we employ a no-regret formulation,
approximated through a series of low-regret problems. This approach enables the construction of deformation fields that are robust to incomplete boundary information. The formulation leverages the Fenchel transform, and we analyze the convergence of solutions from the low-regret to the no-regret problem. Additionally, the gradient of the cost is characterized, and a first-order numerical method is proposed. Numerical examples highlight the robustness of the low-regret deformation fields against missing data, providing what is likely the first numerical investigation of the effectiveness of the low-regret approach in such optimal control problems.