A penalty decomposition method for the optimization problem with two 0-norm constraints

摘要

In this paper, we extend the l_0 minimization problem to a special sparse approximation problem in which contains two l_0 - norm constraints to control the sparsities of different parts of the solution. We introduce the first-order optimality conditions for this problem, and propose a penalty decomposition algorithm to solve this problem. We prove that our algorithm can find a local minimizer of the problem under some suitable assumptions.