Lieven Vandenberghe, University of California, Los Angeles

Abstract

We discuss entropic proximal methods for convex optimization problems over the cone of nonnegative trigonometric polynomials. Problems of this type arise in signal processing and system identification. They can be handled by interior-point methods for semidefinite optimization, at a computational cost that it is at least cubic in the degree of the polynomial.

In the talk we will examine proximal methods with a lower complexity per iteration.  The methods use the Itakura-Saito distance measure as a Bregman divergence.  This choice is motivated by the possibility of computing the associated generalized projection at the cost of solving a small number of positive definite Toeplitz systems.

The complexity per iteration of the resulting proximal algorithms is therefore roughly quadratic in the degree of the polynomial.

Joint work with Hsiao-Han Chao.

Slides     Video