Title: An Optimization Framework with Flexible Inexact Inner Iterations for Nonconvex and Nonsmooth Programming,
Abstract: In recent years, numerous vision and learning tasks have been (re)formulated
as nonconvex and nonsmooth programmings(NNPs). Although some algorithms have
been proposed for particular problems, designing fast and flexible optimization
schemes with theoretical guarantee is a challenging task for general NNPs. It
has been investigated that performing inexact inner iterations often benefit to
special applications case by case, but their convergence behaviors are still
unclear. Motivated by these practical experiences, this paper designs a novel
algorithmic framework, named inexact proximal alternating direction method
(IPAD) for solving general NNPs. We demonstrate that any numerical algorithms
can be incorporated into IPAD for solving subproblems and the convergence of
the resulting hybrid schemes can be consistently guaranteed by a series of
simple error conditions. Beyond the guarantee in theory, numerical experiments
on both synthesized and real-world data further demonstrate the superiority and
flexibility of our IPAD framework for practical use.