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

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 p...

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Vydáno v:Journal of global optimization Ročník 87; číslo 2-4; s. 939 - 964
Hlavní autoři: Yang, Xin, Xu, Lingling
Médium: Journal Article
Jazyk:angličtina
Vydáno: New York Springer US 01.11.2023
Springer
Témata:
Algorithms
Computer Science
Mathematics
Mathematics and Statistics
Operations Research/Decision Theory
Optimization
Real Functions
Alternating minimization
Nonconvex-nonsmooth optimization
Accelerated method
Kurdyka–Łojasiewicz (KŁ) property
Convergence analysis
ISSN:0925-5001, 1573-2916
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Popis
Shrnutí: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.
ISSN:0925-5001
1573-2916
DOI:10.1007/s10898-022-01214-3