The following seminar will take place next week; Lauri Nyman and Vanni Noferini from Aalto University are visiting the department of computer science in that week.
Title: Riemann-Oracle: A framework for matrix nearness problems Speaker: Lauri Nyman, Aalto University, Espoo, Finland Where: Sala Seminari Est, Dipartimento di Informatica When: Tuesday December 10, 2024; 16:00
Abstract: In this talk, we propose a versatile approach for addressing a large family of matrix nearness problems. In these problems, the task is to find a matrix nearest to a given one that satisfies a desired constraint. The method is based on splitting a matrix nearness problem into two nested optimization problems, of which the inner one can be solved cheaply and exactly, while the outer one can be recast as an unconstrained optimization task over a smooth real Riemannian manifold. We also show that the objective function to be minimized on the Riemannian manifold can be discontinuous, thus requiring regularization techniques, and we give conditions for this to happen. Finally, we demonstrate the practical applicability of our method by implementing it for a number of matrix nearness problems that are relevant for applications, including nearest singular matrix with a given sparsity structure, nearest singular matrix polynomial, approximate GCD and nearest unstable matrix.