Preconditioned SQP solvers for nonlinear optimization problems with partial differential equations

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Partial differential equations (PDEs) are the language to describe countless phenomena in the natural sciences and engineering. The optimization of such processes, or the identification of unknown model parameters, lead to optimization problems with PDEs. Sequential quadratic programming (SQP) algorithms are powerful and widely used solution methods for nonlinear problems of this type. The overall effectiveness of an SQP algorithm depends on its global and local convergence properties, as well as on the fast solution of the quadratic programming (QP) subproblem in every iteration. In the proposed project, we will investigate a new class of preconditioners which are especially well suited for the efficient solution of the subproblems occuring in the popular composite-step trust-region SQP methods. Our research will thus lead to a new branch of preconditioned matrix-free SQP solvers for nonlinear large-scale optimization problems. Challenging applications governed by nonlinear, coupled and time-dependent PDEs will demonstrate the potential and limitations of these methods.