Journal of Nonlinear and Variational Analysis

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DOI: 10.23952/jnva.10.2026.1.06

Volume 10, Issue 1, 1 April 2026, Pages 139-161

 

Abstract. In this paper, we propose an accelerated alternating structure-adapted proximal gradient descent algorithm for a class of nonconvex and nonsmooth nonseparable problems. The proposed algorithm is a monotone method which combines two-step inertial extrapolation and generalized Bregman distance. Under some assumptions, we prove that every cluster point of the sequence generated by our algorithm is a critical point. Furthermore, with the help of the Kurdyka-Łojasiewicz property, we establish the convergence of the whole sequence generated by proposed algorithm. In order to make the algorithm more effective and flexible, we also use some strategies to update the extrapolation parameter. Moreover, we report some preliminary numerical results on Poisson linear inverse problems to demonstrate the feasibility and effectiveness of the proposed algorithm.

 

How to Cite this Article:
J. Zhao, C. Guo, A two-step inertial Bregman alternating structure-adapted proximal gradient descent algorithm for nonconvex and nonsmooth problems, J. Nonlinear Var. Anal. 10 (2026), 139-161.