Exploiting Geometric Structure in Matrix-Valued Optimization

Explore matrix-valued optimization in machine learning applications through a 58-minute lecture by Melanie Weber. Delve into the advantages of exploiting non-Euclidean structure in optimization problems on Riemannian manifolds subject to convex constraints. Examine classical problems like barycenter and Brascamp-Lieb constant computation, understanding their significance in mathematics and computer science. Learn about Riemannian Frank-Wolfe methods for solving constrained optimization problems on manifolds, including their global, non-asymptotic convergence analysis. Investigate CCCP-style algorithms for Riemannian "difference of convex" functions and their connections to constrained optimization. Apply these concepts to practical problems, gaining insights from joint work with Suvrit Sra in this Applied Algebraic Topology Network presentation.