Stochastic Primal–Dual Hybrid Gradient Algorithm with Adaptive Step Sizes

In this work, we propose a new primal–dual algorithm with adaptive step sizes. The stochastic primal–dual hybrid gradient (SPDHG) algorithm with constant step sizes has become widely applied in large-scale convex optimization across many scientific fields due to its scalability. While the product of...

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Veröffentlicht in:Journal of mathematical imaging and vision Jg. 66; H. 3; S. 294 - 313
Hauptverfasser: Chambolle, Antonin, Delplancke, Claire, Ehrhardt, Matthias J., Schönlieb, Carola-Bibiane, Tang, Junqi
Format: Journal Article
Sprache:Englisch
Veröffentlicht: New York Springer US 01.06.2024
Springer Nature B.V
Springer Verlag
Schlagworte:
Adaptive algorithms
Algorithms
Applications of Mathematics
Computed tomography
Computer Science
Convergence
Convex analysis
Convexity
Image Processing and Computer Vision
Inverse problems
Mathematical Methods in Physics
Mathematics
Signal,Image and Speech Processing
Upper bounds
ISSN:0924-9907, 1573-7683
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Zusammenfassung:In this work, we propose a new primal–dual algorithm with adaptive step sizes. The stochastic primal–dual hybrid gradient (SPDHG) algorithm with constant step sizes has become widely applied in large-scale convex optimization across many scientific fields due to its scalability. While the product of the primal and dual step sizes is subject to an upper-bound in order to ensure convergence, the selection of the ratio of the step sizes is critical in applications. Up-to-now there is no systematic and successful way of selecting the primal and dual step sizes for SPDHG. In this work, we propose a general class of adaptive SPDHG (A-SPDHG) algorithms and prove their convergence under weak assumptions. We also propose concrete parameters-updating strategies which satisfy the assumptions of our theory and thereby lead to convergent algorithms. Numerical examples on computed tomography demonstrate the effectiveness of the proposed schemes.
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ISSN:0924-9907
1573-7683
DOI:10.1007/s10851-024-01174-1