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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 and 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, vol.~29, No~1, p.~933-963. ISSN~1052-6234. Available from: https://dx.doi.org/10.1137/18M1170194.
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