"Optimization on manifolds"
Pierre-Antoine Absil (UCL)
The world abounds with problems that can be formulated as finding an
optimum of a real-valued cost function defined on a nonlinear search
space that admits a differentiable manifold structure. When the
nonlinear manifold is defined as a subset of a Euclidean space, the
optimization-on-manifold approach can be thought of as
solving an unconstrained optimization problem in a nonlinear space
instead of an equality-constrained optimization problem in a linear
space. To be competitive, this approach critically relies on the
existence of numerically tractable local one-to-one mappings between
the nonlinear manifold and a Euclidean space. Fortunately, several
manifolds of great practical relevance admit such mappings.
In this talk, I will give an overview of optimization methods on
manifolds and their applications, with an emphasis on the underlying
geometric concepts and on the numerical efficiency of the algorithm
implementations.
Two OPTEC professors have been awarded three "Gouden Krijtjes", the yearly teaching awards given by the organization of engineering students (vtk). Prof. Lombaert was awarded the prize for the best course in civil engineering, and Prof. Diehl the prizes for the best professor and the best course in mathematical engineering (where he teaches numerical optimization). They received these awards at the yearly "proffentap" where experienced students taught them how to draft beer professionally.
