P59 - A Scalable Interior-Point Method for PDE-Constrained Inverse Problems Subject to Inequality Constraints
DescriptionWe present a scalable computational method for large-scale inverse problems with PDE and inequality constraints. Such problems are used to learn spatially distributed variables that respect bound constraints and parametrize PDE-based models from unknown or uncertain data. We first briefly overview PDE-constrained optimization and highlight computational challenges of Newton-based solution strategies, such as Krylov-subspace preconditioning of Newton linear systems for problems with inequality constraints. These problems are particularly challenging as their respective first order optimality systems are coupled PDE and nonsmooth complementarity conditions. We propose a Newton interior-point method with a robust filter-line search strategy whose performance is independent of the problem discretization. To solve the interior-point Newton linear systems we use a Krylov-subspace method with a block Gauss-Seidel preconditioner. We prove that the number of Krylov-subspace iterations is independent of both the problem discretization as well as any ill-conditioning due to the inequality constraints. We also present computational results, using MFEM and hypre linear solver packages, on an inverse problem wherein the block Gauss-Seidel preconditioner apply requires only a few scalable algebraic multigrid solves and thus permits the scalable solution of the PDE- and bound-constrained example problem. We conclude with future directions and outlook.
TimeTuesday, June 2719:30 - 21:30 CEST