Reduced order solution of structured linear systems arising in certain PDE-constrained optimization problems (Q1928744)

The author investigates solving of structured algebraic linear systems whose blocks stem from the discretized first-order optimality conditions for PDE-constrained optimal control problems. The numerical solution of the corresponding large scale system is analyzed. An ordered reduction is performed firstly and the reduced system is solved iteratively using specifically designed preconditioning techniques. The analysis is completed by numerical experiments on an Dirichlet problem for the Poisson equation and on a simplified Monge-Kantorovich mass transfer problem.