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In recent years, numerous vision and learning tasks have been (re)formulatedas nonconvex and nonsmooth programmings(NNPs). Although some algorithms havebeen proposed for particular problems, designing fast and flexible optimizationschemes with theoretical guarantee is a challenging task for general NNPs. Ithas been investigated that performing inexact inner iterations often benefit tospecial applications case by case, but their convergence behaviors are stillunclear. Motivated by these practical experiences, this paper designs a novelalgorithmic framework, named inexact proximal alternating direction method(IPAD) for solving general NNPs. We demonstrate that any numerical algorithmscan be incorporated into IPAD for solving subproblems and the convergence ofthe resulting hybrid schemes can be consistently guaranteed by a series ofsimple error conditions. Beyond the guarantee in theory, numerical experimentson both synthesized and real-world data further demonstrate the superiority andflexibility of our IPAD framework for practical use.

An Optimization Framework with Flexible Inexact Inner Iterations for Nonconvex and Nonsmooth Programming