MIERCURI, 07.04.2021, la ora 13.30, la Facultatea de Matematică și Informatică a avut loc SEMINARUL ONLINE
Introduction to optimization on manifolds
cu invitatul special Pierre-Antoine Absil,
Institute of Information and Communication Technologies, Electronics and Applied Mathematics (ICTEAM),
Louvain School of Engineering University of Louvain, Belgium. https://sites.uclouvain.be/absil/
ABSTRACT:
This talk concerns applications of differential geometry in numerical
optimization. They arise when the optimization problem can be formulated
as finding an optimum of a real-valued cost function defined on a smooth
nonlinear search space. Oftentimes, the search space is a "matrix
manifold", in the sense that its points admit natural representations in
the form of matrices. In most cases, the matrix manifold structure is
due either to the presence of certain nonlinear constraints (such as
orthogonality or rank constraints), or to invariance properties in the
cost function that need to be factored out in order to obtain a
nondegenerate optimization problem. Manifolds that come up in practical
applications include the rotation group SO(3) (generation of rigid body
motions from sample points), the set of fixed-rank matrices (low-rank
models, e.g., in collaborative filtering), the set of 3x3 symmetric
positive-definite matrices (interpolation of diffusion tensors), and the
shape manifold (morphing).
In the recent years, the practical importance of optimization problems
on manifolds has stimulated the development of geometric optimization
algorithms that exploit the differential structure of the manifold
search space. In this talk, we give an overview of geometric
optimization algorithms and their applications, with an emphasis on the
underlying geometric concepts and on the numerical efficiency of the
algorithm implementations.
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