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

## TL;DR

This paper introduces a new proximally linearized algorithm called InISSAPL designed to efficiently solve non-Lipschitz group sparse optimization problems involving the _{p,q}-_{r} model, ensuring global convergence.

## Contribution

The paper presents the first efficient algorithm with global convergence guarantees for the _{p,q}-_{r} group sparse optimization problem.

## Key findings

- The algorithm converges globally for the non-Lipschitz _{p,q}-_{r} model.
- It outperforms existing methods in efficiency and accuracy.
- The method is applicable to various group sparse optimization tasks.

## Abstract

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