An accelerated preconditioned primal-dual gradient algorithm for structured nonconvex optimization problems

•An novel accelerated preconditioned primal-dual gradient algorithm for solving nonconvex optimization problems by the conjugate duality theory of nonconvex functions.•Our algorithm only needs to calculate the proximal mapping of the conjugate function which is always convex and lower semicontinuous...

Full description

Saved in:

Bibliographic Details
Published in:	Communications in nonlinear science & numerical simulation Vol. 153; p. 109480
Main Authors:	Long, Xian-Jun, Nie, Jia-Lin, Gou, Zhun, Sun, Xiang-Kai, Li, Gao-Xi
Format:	Journal Article
Language:	English
Published:	Elsevier B.V 01.02.2026
Subjects:	Conjugate duality theory Global convergence Kurdyka-Łojasiewicz property Primal-dual gradient algorithm Structured nonconvex and nonsmooth problem Structured nonconvex and nonsmooth problem Global convergence Kurdyka-Łojasiewicz property 90C30 90C33 Primal-dual gradient algorithm 90C26 Conjugate duality theory
ISSN:	1007-5704
Online Access:	Get full text
Tags:	Add Tag No Tags, Be the first to tag this record!

Description
Summary:	•An novel accelerated preconditioned primal-dual gradient algorithm for solving nonconvex optimization problems by the conjugate duality theory of nonconvex functions.•Our algorithm only needs to calculate the proximal mapping of the conjugate function which is always convex and lower semicontinuous and it does not need to calculate the proximal mapping of nonconvex functions. the computation load may be significantly reduced.•Global convergence under Kurdyka-Lojasiewicz condition.•Numerical results illustrate that the proposed algorithm is quite competitive with some existing algorithms. For a nonconvex problem, the computation of the proximal operator of the nonconvex function is difficult in general. In this paper, based on the conjugate duality theory of nonconvex functions, we present an accelerated preconditioned primal-dual gradient algorithm for a class of nonconvex optimization problems. Compared with the existing algorithms, our algorithm only needs to calculate the proximal mapping of the conjugate function which is always convex and lower semicontinuous and it does not need to calculate the proximal mapping of nonconvex functions. Hence, the computation load may be significantly reduced. We prove that the sequence generated by the proposed algorithm globally converges to a critical point under Kurdyka-Łojasiewicz framework. Furthermore, we derive the convergence rate of the proposed algorithm. Finally, numerical results on signal recovery, image denoising and sparse principal component analysis illustrate that the proposed algorithm is quite competitive with some existing algorithms.
ISSN:	1007-5704
DOI:	10.1016/j.cnsns.2025.109480