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The stochastic primal\u2013dual 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.\n<\/jats:p>","DOI":"10.1007\/s10851-024-01174-1","type":"journal-article","created":{"date-parts":[[2024,3,16]],"date-time":"2024-03-16T13:01:46Z","timestamp":1710594106000},"page":"294-313","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":19,"title":["Stochastic Primal\u2013Dual Hybrid Gradient Algorithm with Adaptive Step Sizes"],"prefix":"10.1007","volume":"66","author":[{"given":"Antonin","family":"Chambolle","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Claire","family":"Delplancke","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Matthias J.","family":"Ehrhardt","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Carola-Bibiane","family":"Sch\u00f6nlieb","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Junqi","family":"Tang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2024,3,16]]},"reference":[{"issue":"2","key":"1174_CR1","doi-asserted-by":"publisher","first-page":"1288","DOI":"10.1137\/19M1296252","volume":"32","author":"A Alacaoglu","year":"2022","unstructured":"Alacaoglu, A., Fercoq, O., Cevher, V.: On the convergence of stochastic primal-dual hybrid gradient. 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