Title: A Unified Framework for Establishing Error Bounds for
Structured Convex Optimization Problems

Speaker: Anthony Man-Cho So, Chinese University of Hong Kong

Time/Date: Friday, Apr 8, 11-12

Location: 3501

Abstract:

In recent years, we have witnessed a widespread use of first-order
methods (FOMs) to solve large-scale structured convex optimization
problems. It is well known that many FOMs will converge linearly if
the problem at hand possesses a certain Lipschitzian error bound. In
this talk, we shall present a new framework for establishing such
error bounds for a host of structured convex optimization problems.
Our framework makes essential use of the notions of calmness and
metric subregularity from variational analysis. It not only unifies
and simplifies the proofs of several existing error bounds but also
leads to a new error bound for structured convex optimization with
nuclear norm regularization. We believe that our techniques will have
further applications in the development of error bounds and
convergence rate analysis of first-order methods.