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Seminar description: 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. |
