Research Areas

Matthias Heinkenschloss’ research interests are in the design and analysis of mathematical optimization algorithms for nonlinear, large-scale (often infinite dimensional) problems and their applications to science and engineering problems. Research areas include large-scale nonlinear optimization, model order reduction, optimal control of partial differential equations (PDEs), optimization under uncertainty, PDE constrained optimization, iterative solution of KKT systems and domain decomposition in optimization.

Industry Impact & Relevance

Matthias Heinkenschloss’ research focuses on the development of theoretically founded, computationally efficient numerical algorithms for large-scale nonlinear optimization problems and their applications to engineering and science problems. Such optimization problems arise, e.g., in the form of parameter identification problems, where one needs to infer properties of the system from observations of the system output, in the form of optimal control problems, where one wants to compute system inputs to optimize system performance, or in the form optimal design problems, where one wants to design (parts of) the system to optimize system performance. Examples include flow control, reservoir management, shell structure acoustic optimization, imaging, and shape optimization. These optimization problems are governed by complex simulations, which often require the solution of differential equations. Often these optimization problems are subject to uncertainty in system parameters or operating conditions. The optimization approaches developed in Dr. Heinkenschloss’ group rigorously integrate state-of-the optimization algorithms with the underlying differential equations and their discretizations. This integrative approach allows efficient extraction of problem information required for optimization and substantially expands the ability to solve optimization problems governed by complex simulations. Research on linear system solvers and model reduction addresses critical bottlenecks in the optimization solution process. Specifically, data-driven model reduction approaches systematically extract information from observations of complex simulations needed for decision making, and have the potential to circumvent complex simulations while still providing solution fidelity requested by the user.