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In various fields such as engineering, science, and medicine, numerous phenomena can be described through the solution of partial differential equations (PDEs) or systems of PDEs. Historically, much research has centered around numerically solving these PDEs. The recent advancements in algorithms and computing technology have lead to a surge in interest towards solving optimal control problems constrained by PDEs. The goal in PDE-constrained optimization is to determine the parameters for a particular PDE or systems of PDEs such that a given objective function is minimized. This discipline is part of infinite-dimensional optimization, as solutions to PDE belong to an infinite-dimensional space. In this seminar we will focus on two important applications of PDE-constrained optimization problems: inverse problems, where the aim is to recover a set of parameters from measurement data, and shape optimization problems, which are optimization problems with respect to the geometry. |
