An augmented Lagrangian proximal alternating method for sparse discrete optimization problems

In this paper, we propose an augmented Lagrangian proximal alternating (ALPA) method for solving two classes of large-scale sparse discrete constrained optimization problems. Specifically, the ALPA method generates a sequence of augmented Lagrangian (AL) subproblems in the out iterations and utilizes a proximal alternating linearized minimization method and sparse projection techniques to solve these AL subproblems. And we study the first-order optimality conditions for these two classes of problems. Under some suitable assumptions, we show that any accumulation point of the sequence generated by the ALPA method satisfies the necessary first-order optimality conditions of these problems or is a local minimizer of these problems. 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.