Four perspectives on the numerical solution of PDE-constrained optimization problems

John Pearson (The University of Kent)


PDE-constrained optimization problems have a wide range of applications across numerical mathematics and applied science, so it is important to develop fast and feasible methods to solve such problems. We employ preconditioned iterative methods to tackle the large and sparse matrix systems that arise from their discretization, and consider a range of issues related to these solvers. In particular, we discuss applications of reaction-diffusion control problems in chemistry and biology, strategies for handling additional box constraints on the PDE variables, approaches for problems involving fractional derivatives, and deferred correction methods for time-dependent problems.‚Äč

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