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• W3100175597 abstract "The primal--dual hybrid gradient method (PDHGM, also known as the Chambolle--Pock method) has proved very successful for convex optimization problems involving linear operators arising in image processing and inverse problems. In this paper, we analyze an extension to nonconvex problems that arise if the operator is nonlinear. Based on the idea of testing, we derive new step length parameter conditions for the convergence in infinite-dimensional Hilbert spaces and provide acceleration rules for suitably (locally and/or partially) monotone problems. Importantly, we prove linear convergence rates as well as global convergence in certain cases. We demonstrate the efficacy of these step length rules for PDE-constrained optimization problems." @default.
• W3100175597 created "2020-11-23" @default.
• W3100175597 creator A5011665383 @default.
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• W3100175597 date "2019-01-01" @default.
• W3100175597 modified "2023-10-04" @default.
• W3100175597 title "Acceleration and Global Convergence of a First-Order Primal-Dual Method for Nonconvex Problems" @default.
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• W3100175597 doi "https://doi.org/10.1137/18m1170194" @default.
• W3100175597 hasPublicationYear "2019" @default.
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