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@article{1641978, author = {Clason, Christian and Mazurenko, Stanislav and Valkonen, Tuomo}, article_location = {PHILADELPHIA}, article_number = {1}, doi = {http://dx.doi.org/10.1137/18M1170194}, keywords = {acceleration; convergence; global; primal-dual; first order; nonconvex}, language = {eng}, issn = {1052-6234}, journal = {SIAM JOURNAL ON OPTIMIZATION}, title = {ACCELERATION AND GLOBAL CONVERGENCE OF A FIRST-ORDER PRIMAL-DUAL METHOD FOR NONCONVEX PROBLEMS}, url = {https://epubs.siam.org/doi/10.1137/18M1170194}, volume = {29}, year = {2019} }
TY - JOUR ID - 1641978 AU - Clason, Christian - Mazurenko, Stanislav - Valkonen, Tuomo PY - 2019 TI - ACCELERATION AND GLOBAL CONVERGENCE OF A FIRST-ORDER PRIMAL-DUAL METHOD FOR NONCONVEX PROBLEMS JF - SIAM JOURNAL ON OPTIMIZATION VL - 29 IS - 1 SP - 933-963 EP - 933-963 PB - SIAM PUBLICATIONS SN - 10526234 KW - acceleration KW - convergence KW - global KW - primal-dual KW - first order KW - nonconvex UR - https://epubs.siam.org/doi/10.1137/18M1170194 L2 - https://epubs.siam.org/doi/10.1137/18M1170194 N2 - The primal-dual hybrid gradient method, modified (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. ER -
CLASON, Christian, Stanislav MAZURENKO a Tuomo VALKONEN. ACCELERATION AND GLOBAL CONVERGENCE OF A FIRST-ORDER PRIMAL-DUAL METHOD FOR NONCONVEX PROBLEMS. \textit{SIAM JOURNAL ON OPTIMIZATION}. PHILADELPHIA: SIAM PUBLICATIONS, 2019, roč.~29, č.~1, s.~933-963. ISSN~1052-6234. Dostupné z: https://dx.doi.org/10.1137/18M1170194.
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