Constrained composite optimization and augmented Lagrangian methods

Abstract We investigate finite-dimensional constrained structured optimization problems, featuring composite objective functions and set-membership constraints. Offering an expressive yet simple language, this problem class provides a modeling framework for variety of applications. study stationarity regularity concepts, propose flexible augmented Lagrangian scheme. provide theoretical characterization the algorithm its asymptotic properties, deriving convergence results fully nonconvex problems. It is demonstrated how inner subproblems can be solved by off-the-shelf proximal methods, notwithstanding possibility to adopt any solvers, insofar as they return approximate stationary points. Finally, we describe our matrix-free implementation proposed test it numerically. Illustrative examples show versatility programs tool expose difficulties arising in vast class.