Seminar Details
2011-02-01 (15.00) : Derivative-Free Optimization on Matrix Manifolds: Introduction and applications
At Euler building
Organized by Mathematical Engineering
Speaker :
Borckmans, Pierre
Abstract :
Optimization on manifolds is a recent field that is gaining more and more interest. Many applications can naturally be expressed on manifolds,
in order to tackle structure constraints (orthogonality, ...) or invariance properties (rotation, scaling, ...). However, some of these problems may be
non-smooth or non-differentiable, therefore preventing the legit/efficient use of classical optimization algorithms on manifolds (Descent, Newton, ...).
In this talk, we focus on derivative-free optimization on Riemannian manifolds. We briefly present the concept of optimization on manifold, then we
focus on a specific algorithm, namely Particle Swarm Optimization (PSO). We show how PSO can be adapted to matrix manifolds, before applying it
to two practical applications: (1) Oriented Bounding Box Computation (P.B.Borckmans and P.-A. Absil), (2) Low Multilinear-Rank Tensor Approximation
(P.B.Borckmans, M. Isheva and P.-A.Absil). These two problems illustrate the feasibility of the proposed method.