An Augmented Lagrangian Proximal Alternating Method for Sparse Discrete Optimization Problems

In this paper, an augmented Lagrangian proximal alternating (ALPA) method is proposed for two class of large-scale sparse discrete constrained optimization problems in which a sequence of augmented Lagrangian subproblems are solved by utilizing proximal alternating linearized minimization framework and sparse projection techniques. Under the MangasarianFromovitz and the basic constraint qualification , we show that any local minimizer is a Karush-Kuhn-Tuker (KKT) point of the problem. And under some suitable assumptions, any accumulation point of the sequence generated by the ALPA method is a KKT point or a local minimizer of the original problem. The computational results with practical problems demonstrate that our method can find the suboptimal solutions of the problems efficiently and is competitive with some other local solution methods.