ArticleJournal of mathematical imaging and vision2024
Stochastic Primal-Dual Hybrid Gradient Algorithm with Adaptive Step Sizes.
Article in Journal of mathematical imaging and vision, 2024. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Not yet cited in PubMed.
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Abstract
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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