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Article

Proximal Linearized Iteratively Reweighted Algorithms for Nonconvex and Nonsmooth Optimization Problem

by
Juyeb Yeo
and
Myeongmin Kang
*
Department of Mathematics, Chungnam National University, Daejeon 34134, Korea
*
Author to whom correspondence should be addressed.
Axioms 2022, 11(5), 201; https://doi.org/10.3390/axioms11050201
Submission received: 20 March 2022 / Revised: 9 April 2022 / Accepted: 20 April 2022 / Published: 24 April 2022
(This article belongs to the Special Issue Advances in Nonlinear and Convex Analysis)
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Abstract

The nonconvex and nonsmooth optimization problem has been attracting increasing attention in recent years in image processing and machine learning research. The algorithm-based reweighted step has been widely used in many applications. In this paper, we propose a new, extended version of the iterative convex majorization–minimization method (ICMM) for solving a nonconvex and nonsmooth minimization problem, which involves famous iterative reweighted methods. To prove the convergence of the proposed algorithm, we adopt the general unified framework based on the Kurdyka–Łojasiewicz inequality. Numerical experiments validate the effectiveness of the proposed algorithm compared to the existing methods.
Keywords: iterative reweighted algorithm; linearization; nonconvex optimization; nonsmooth objective function; Kurdyka–Łojasiewicz property iterative reweighted algorithm; linearization; nonconvex optimization; nonsmooth objective function; Kurdyka–Łojasiewicz property

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MDPI and ACS Style

Yeo, J.; Kang, M. Proximal Linearized Iteratively Reweighted Algorithms for Nonconvex and Nonsmooth Optimization Problem. Axioms 2022, 11, 201. https://doi.org/10.3390/axioms11050201

AMA Style

Yeo J, Kang M. Proximal Linearized Iteratively Reweighted Algorithms for Nonconvex and Nonsmooth Optimization Problem. Axioms. 2022; 11(5):201. https://doi.org/10.3390/axioms11050201

Chicago/Turabian Style

Yeo, Juyeb, and Myeongmin Kang. 2022. "Proximal Linearized Iteratively Reweighted Algorithms for Nonconvex and Nonsmooth Optimization Problem" Axioms 11, no. 5: 201. https://doi.org/10.3390/axioms11050201

APA Style

Yeo, J., & Kang, M. (2022). Proximal Linearized Iteratively Reweighted Algorithms for Nonconvex and Nonsmooth Optimization Problem. Axioms, 11(5), 201. https://doi.org/10.3390/axioms11050201

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