Tutte Colloquium - Minh Bui

Title: Warped Proximal Iterations for Multivariate Convex Minimization in Hilbert Spaces

Abstract:

We propose a multivariate convex minimization model which involves a mix of nonsmooth and smooth functions, as well as linear mixtures of the variables. This formulation captures a wide range of concrete scenarios in the literature. A limitation of existing methods is that they do not achieve full splitting of our problem in the sense that each function and linear operator is activated separately. To circumvent this issue, we propose a novel approach, called warped proximal iterations, for solving this problem. This leads to a highly flexible proximal method, which achieves full splitting, exploits the specific attribute of each function, is asynchronous, and requires to activate only a block of functions at each iteration, as opposed to activating all of them as in standard methods. The last feature is of critical importance in large-scale problems.

Based on joint work with Patrick L. Combettes.