Nov 6 – 8, 2019
MPI Magdeburg
Europe/Berlin timezone

Multilevel optimization on low-rank manifolds for optimal control problems

Not scheduled
25m
Prigogine (MPI Magdeburg)

Prigogine

MPI Magdeburg

MPI for Dynamics of Complex Technical Systems Sandtorstr. 1 39106 Magdeburg
Talk Talks Day III

Speaker

Marco Sutti (University of Geneva)

Description

Large-scale finite-dimensional optimization problems arising from the discretization of problems involving PDEs (like in optimal control problems) sometimes admit solutions that can be well approximated by low-rank matrices. In this talk, we will exploit this low-rank approximation property by solving the optimization problem directly over the set of low-rank matrices. In particular, we introduce a new multilevel algorithm, where the optimization variable is constrained to the Riemannian manifold of fixed-rank matrices. In contrast to other multilevel low-rank algorithms where the rank is chosen adaptively on each level, we can keep the ranks (and thus the computational complexity) fixed throughout the iterations. Classical implementation of line-search based on Wolfe conditions allows computing a solution with numerical accuracy in the order of the square root of the machine epsilon. Here we adopt approximate Wolfe conditions that allow computing a solution on the order of the machine epsilon. Numerical experiments demonstrate the computational efficiency of the proposed framework. This is joint work with Bart Vandereycken.

Primary author

Marco Sutti (University of Geneva)

Co-author

Bart Vandereycken (University of Geneva)

Presentation materials

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