摘要 : Noncontinuous and nonconvex t0 sparsity-induced problems generally are NP-hard since the discrete combinatorial nature. Best performing approaches commonly leverage con-vex/nonconvex relaxation schemes to solve this combinatorial ... 展开 Noncontinuous and nonconvex t0 sparsity-induced problems generally are NP-hard since the discrete combinatorial nature. Best performing approaches commonly leverage con-vex/nonconvex relaxation schemes to solve this combinatorial optimization problem. In this paper, we establish a general unified framework to cover these relaxation schemes; not only that, but we also integrate an exact variational reformulation of t0 pseudo-norm into this framework. Specifically, we apply locally Lipschitz continuous scaled folded concave functions to approximate t0 pseudo-norm. A generic nonsmooth but convex framework is established to gradually approximate the scaled folded concave functions based on the Legendre-Fenchel transformation. Furthermore, the exact variational (com-plementarity) reformulation to t0 pseudo-norm is integrated into this framework by proving the relationship between these two relaxation methods. A two-doubly primal- dual iterative algorithm is established based on these frameworks, and the convergence of the proposed algorithms is also being analyzed. Numerical experimental result shows the proposed framework and algorithms admit the exact sparsity-induced capability of t0 pseudo-norm.(c) 2022 Elsevier B.V. All rights reserved. 收起