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On the implementation of ADMM with dynamically configurable parameter for the separable \(\ell _{1}/\ell _{2}\) minimization

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Abstract

In this paper, we propose a novel variant of the alternating direction method of multipliers (ADMM) approach for solving minimization of the rate of \(\ell _{1}\) and \(\ell _{2}\) norms for sparse recovery. We first transform the quotient of \(\ell _{1}\) and \(\ell _{2}\) norms into a new function of the separable variables using the least squares minimum norm solution of the linear system of equations. Subsequently, we employ the augmented Lagrangian function to formulate the corresponding ADMM method with a dynamically adjustable parameter. Additionally, each of its subproblems possesses a unique global minimum. Finally, we present some numerical experiments to demonstrate our results.

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Acknowledgements

We are very grateful to anonymous reviewers for their constructive suggestions which improved this paper significantly. The research of Jun Wang has been supported by Scientific Startup Foundation for Doctors of Jiangsu University of Science and Technology (CN) (No. 1052931903). The work of Qiang Ma has been supported by Scientific Startup Foundation for Doctors of Jiangsu University of Science and Technology (CN) (No. 1062931902), the National Natural Science Foundation of China (NSFC) under Grants (No. 52105350) and State Laboratory of Advanced Welding and Joining in HIT (CN) (AWJ-23R01).

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Authors and Affiliations

  1. School of Science, Jiangsu University of Science and Technology, Zhenjiang, 212003, China

    Jun Wang

  2. School of Materials Science and Engineering, Jiangsu University of Science and Technology, Zhenjiang, 212003, China

    Jun Wang & Qiang Ma

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  1. Jun Wang
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  2. Qiang Ma
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Correspondence to Jun Wang.

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Wang, J., Ma, Q. On the implementation of ADMM with dynamically configurable parameter for the separable \(\ell _{1}/\ell _{2}\) minimization. Optim Lett (2024). https://doi.org/10.1007/s11590-024-02106-z

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