ACCELERATION AND GLOBAL CONVERGENCE OF A FIRST-ORDER PRIMAL-DUAL METHOD FOR NONCONVEX PROBLEMS
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14310%2F19%3A00113487" target="_blank" >RIV/00216224:14310/19:00113487 - isvavai.cz</a>
Result on the web
<a href="https://epubs.siam.org/doi/10.1137/18M1170194" target="_blank" >https://epubs.siam.org/doi/10.1137/18M1170194</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1137/18M1170194" target="_blank" >10.1137/18M1170194</a>
Alternative languages
Result language
angličtina
Original language name
ACCELERATION AND GLOBAL CONVERGENCE OF A FIRST-ORDER PRIMAL-DUAL METHOD FOR NONCONVEX PROBLEMS
Original language description
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.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10102 - Applied mathematics
Result continuities
Project
—
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2019
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
SIAM JOURNAL ON OPTIMIZATION
ISSN
1052-6234
e-ISSN
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Volume of the periodical
29
Issue of the periodical within the volume
1
Country of publishing house
US - UNITED STATES
Number of pages
31
Pages from-to
933-963
UT code for WoS article
000462593800036
EID of the result in the Scopus database
2-s2.0-85065421654