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

Hongtao Li, Wenxing Zhu


In this paper, we extend the l0 minimization problem to a special sparse approximation problem in which contains two l0 − 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


l0 − norm, sparsity control, block coordinate descent method, penalty decomposition.

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