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Group sparsity combines the underlying sparsity and group structure of thedata in problems. We develop a proximally linearized algorithm InISSAPL for thenon-Lipschitz group sparse $\ell_{p,q}$-$\ell_r$ optimization problem.

An Efficient and Globally Convergent Algorithm for $\ell_{p,q}$-$\ell_{r}$ Model in Group Sparse Optimization