@article{Kang2026, 
author = {Myeongmin Kang},
title = {An inertial generalized iteratively reweighted        ℓ    1   algorithm for nonconvex and nonsmooth optimization},
year = {2026},
journal = {AIMS Mathematics},
volume = {11},
number = {6},
pages = {16414-16447},
keywords = {iteratively reweighted ℓ1 algorithm, inertial extrapolation, co-coercivity, nonconvex optimization, Kurdyka–Łojasiewicz property},
url = {https://www.sciopen.com/article/10.3934/math.2026674},
doi = {10.3934/math.2026674},
abstract = {We study a class of nonconvex and nonsmooth optimization problems arising in sparse recovery and related applications, which are often addressed using iteratively reweighted        ℓ    1   (IRL1)-type algorithms. Classical IRL1 methods are typically developed under a Lipschitz gradient assumption, which may limit their applicability. In this paper, we propose a generalized iteratively reweighted        ℓ    1   algorithm with inertial extrapolation (GIRL1E), where the generalization is based on a co-coercivity condition imposed on the smooth component, thereby allowing a broader class of problems to be treated. By integrating inertial extrapolation into the generalized IRL1 framework, we establish global convergence of the proposed algorithm to a critical point of the objective function. In particular, we prove a sufficient descent property of an associated Lyapunov function and the convergence of the entire sequence without assuming convexity. Numerical experiments on compressive sensing-based signal recovery and image deblurring demonstrated that GIRL1E consistently achieves improved practical performance compared with existing IRL1 methods.}
}