DATE2023-11-02 16:10-17:00

PLACE數學系館 1F3174教室

SPEAKERDr. Marco Sutti(國家理論科學研究中心

TITLENumerical Optimization on Matrix Manifolds

ABSTRACT In this talk, we will showcase several fundamental ideas and tools needed to perform numerical optimization on matrix manifolds. We will start with a brief overview of the steepest descent method, a classical optimization algorithm in Euclidean space. Then, we will introduce the main tools from Riemannian geometry that allow us to extend the steepest descent to matrix manifolds, with particular emphasis on retraction mapping, and present some numerical examples. To keep the presentation more concrete, we will fix our ideas on the Stiefel manifold, but the concepts discussed herein would remain valid for any embedded submanifold. If time permits, we will also discuss the manifold of fixed-rank matrices and some related applications.