Inertial self-adaptive algorithms for solving non-smooth convex optimization problems

In this paper, for two different forms of non-smooth convex optimization problems, we investigate the self-adaptive algorithms with inertia acceleration. Firstly, we propose a self-adaptive proximal gradient algorithm with an inertial step. Under reasonable parameters, the strong convergence theorem...

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Vydáno v:Numerical algorithms Ročník 98; číslo 1; s. 133 - 163
Hlavní autoři: Chen, Xin, Duan, Peichao
Médium: Journal Article
Jazyk:angličtina
Vydáno: New York Springer US 01.01.2025
Springer Nature B.V
Témata:
Adaptive algorithms
Algebra
Algorithms
Computer Science
Convergence
Convex analysis
Convexity
Hilbert space
Numeric Computing
Numerical Analysis
Optimization
Original Paper
Theory of Computation
Viscosity
Inertial acceleration
49J53
Convex optimization
90C25
Split proximal algorithm
47H09
65K10
Self-adaptive algorithm
Proximal gradient algorithm
ISSN:1017-1398, 1572-9265
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Shrnutí:In this paper, for two different forms of non-smooth convex optimization problems, we investigate the self-adaptive algorithms with inertia acceleration. Firstly, we propose a self-adaptive proximal gradient algorithm with an inertial step. Under reasonable parameters, the strong convergence theorem is established. Secondly, we propose a self-adaptive split proximal algorithm with inertial acceleration. We prove that our algorithm converges strongly under suitable conditions. Notably, both inertial algorithms are extended to multi-step inertial version to accelerate the convergence of the algorithms. Finally, numerical results illustrate the performances of our algorithms.
Bibliografie:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:1017-1398
1572-9265
DOI:10.1007/s11075-024-01788-x