University of North Carolina
Tuesday, June 21, 2016, 11:00
Room 01-012, Georges-Köhler-Allee 102, Freiburg 79110, Germany
In this talk, we present a joint treatment between the proximal operator and the self-concordance notion to develop a class of proximal path-following and interior-point methods for solving [nonsmooth] constrained convex optimization problems. While the proximal operator plays a central role for developing several first-order and splitting optimization algorithms, the self-concordance concept is key to unify and analyze polynomial time worst-case complexity in interior-point methods. To the best of our knowledge, these concepts have not been exploited in a unified framework for designing optimization algorithms.
We propose a second order optimization framework using both proximal operators and self-concordant barriers to design new algorithms for solving composite convex minimization as well as (nonsmooth) constrained convex optimization problems. Then, we specify and extend this framework to obtain different algorithms such as primal, dual and primal-dual methods for handling different problem settings. We also identify some examples where this approach is useful compared to existing state-of-the-art schemes.