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DTSTAMP:20230831T095746Z
LOCATION:Hall
DTSTART;TZID=Europe/Stockholm:20230627T193000
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UID:submissions.pasc-conference.org_PASC23_sess116_pos121@linklings.com
SUMMARY:P59 - A Scalable Interior-Point Method for PDE-Constrained Inverse
  Problems Subject to Inequality Constraints
DESCRIPTION:Poster\n\nTucker Hatland and Cosmin Petra (Lawrence Livermore 
 National Laboratory), Noemi Petra (University of California Merced), and J
 ingyi Wang (Lawrence Livermore National Laboratory)\n\nWe present a scalab
 le computational method for large-scale inverse problems with PDE and ineq
 uality 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 soluti
 on strategies, such as Krylov-subspace preconditioning of Newton linear sy
 stems for problems with inequality constraints. These problems are particu
 larly challenging as their respective first order optimality systems are c
 oupled PDE and nonsmooth complementarity conditions. We propose a Newton i
 nterior-point method with a robust filter-line search strategy whose perfo
 rmance 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 i
 terations is independent of both the problem discretization as well as any
  ill-conditioning due to the inequality constraints. We also present compu
 tational results, using MFEM and hypre linear solver packages, on an inver
 se problem wherein the block Gauss-Seidel preconditioner apply requires on
 ly a few scalable algebraic multigrid solves and thus permits the scalable
  solution of the PDE- and bound-constrained example problem. We conclude w
 ith future directions and outlook.
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