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Keywords: Optimization; Partial Differential Equations; Numerical Methods; Optimal Control; Optimality Theory
Organizers:
Tim Suchan (1) – suchan@hsu-hh.de
Estefania Loayza-Romero (2) – k.loayza-romero@imperial.ac.uk
Affiliations:
(1) Helmut Schmidt University / University of the Federal Armed Forces Hamburg, Germany
(2) Department of Mathematics and Statistics, University of Strathclyde, UK
Abstract:
The already challenging nature of nonlinear optimization—characterized by issues such as multiple minima, nondifferentiable objective functions, and constraints on optimization variables—becomes even more complex when coupled with partial differential equations (PDE) that describe the underlying physical processes. Optimization problems involving PDE are prevalent in everyday life, and their applications range from relatively straightforward tasks, like optimizing the cooling of a structure, to determining the interior structure or properties of a body by measurements, to complex challenges, such as producing accurate weather forecasts from measurement data. Another prominent example is structural design, where the main goal is to find the geometry of a structure that satisfies certain optimality criteria. In this case, the behaviour of the materials and structures is modelled by linear or nonlinear PDE. The corresponding problem is thus highly non-convex with multiple minima whose solutions can only be obtained via numerical methods.
Sophisticated algorithms play a critical role in addressing these challenges. They are specifically designed to handle large-scale computations, navigate multiple minima, and deliver robust solutions, even in the presence of uncertainties. These features make them indispensable for tackling real-world optimization problems.
This minisymposium aims to highlight recent advancements in algorithms designed to solve PDE-constrained optimization problems, with applications spanning academic research and industrial challenges. Special emphasis is also placed on methods addressing nonsmoothness, uncertainty quantification, and the integration of artificial intelligence. We further particularly welcome contributions exploring interdisciplinary approaches and computational strategies that push the boundaries of scalability and efficiency in solving real-world problems.