Some accelerated alternating proximal gradient algorithms for a class of nonconvex nonsmooth problems

Xin Yang () and Lingling Xu ()
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Xin Yang: Zhejiang University
Lingling Xu: Nanjing Normal University

Journal of Global Optimization, 2023, vol. 87, issue 2, No 26, 939-964

Abstract: Abstract In this paper, we study a class of nonconvex and nonsmooth optimization problems, whose objective function can be split into two separable terms and one coupling term. Alternating proximal gradient methods combining with extrapolation are proposed to solve such problems. Under some assumptions, we prove that every cluster point of the sequence generated by our algorithms is a critical point. Furthermore, if the objective function satisfies Kurdyka–Łojasiewicz property, the generated sequence is globally convergent to a critical point. In order to make the algorithm more effective and flexible, we also use some strategies to update the extrapolation parameter and solve the problems with unknown Lipschitz constant. Numerical experiments demonstrate the effectiveness of our algorithms.

Keywords: Nonconvex-nonsmooth optimization; Alternating minimization; Accelerated method; Kurdyka–Łojasiewicz (KŁ) property; Convergence analysis (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s10898-022-01214-3

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