Inexact proximal gradient algorithm with random reshuffling for nonsmooth optimization

Proximal gradient algorithms are popularly implemented to achieve convex optimization with nonsmooth regularization. Obtaining the exact solution of the proximal operator for nonsmooth regularization is challenging because errors exist in the computation of the gradient; consequently, the design and...

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Vydáno v:Science China. Information sciences Ročník 68; číslo 1; s. 112201
Hlavní autoři: Jiang, Xia, Fang, Yanyan, Zeng, Xianlin, Sun, Jian, Chen, Jie
Médium: Journal Article
Jazyk:angličtina
Vydáno: Beijing Science China Press 01.01.2025
Springer Nature B.V
Témata:
Algorithms
Basic converters
Computational geometry
Computer Science
Convex analysis
Convexity
Design optimization
Errors
Exact solutions
Information Systems and Communication Service
Neighborhoods
Optimization techniques
Regularization
Research Paper
Signal processing
compressed sensing
inexact computation
nonsmooth optimization
proximal operator
random reshuffling
ISSN:1674-733X, 1869-1919
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Shrnutí:Proximal gradient algorithms are popularly implemented to achieve convex optimization with nonsmooth regularization. Obtaining the exact solution of the proximal operator for nonsmooth regularization is challenging because errors exist in the computation of the gradient; consequently, the design and application of inexact proximal gradient algorithms have attracted considerable attention from researchers. This paper proposes computationally efficient basic and inexact proximal gradient descent algorithms with random reshuffling. The proposed stochastic algorithms take randomly reshuffled data to perform successive gradient descents and implement only one proximal operator after all data pass through. We prove the convergence results of the proposed proximal gradient algorithms under the sampling-without-replacement reshuffling scheme. When computational errors exist in gradients and proximal operations, the proposed inexact proximal gradient algorithms can converge to an optimal solution neighborhood. Finally, we apply the proposed algorithms to compressed sensing and compare their efficiency with some popular algorithms.
Bibliografie:ObjectType-Article-1
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ISSN:1674-733X
1869-1919
DOI:10.1007/s11432-023-4095-y