ACCELERATION AND GLOBAL CONVERGENCE OF A FIRST-ORDER
PRIMAL-DUAL METHOD FOR NONCONVEX PROBLEMS

J 2019

ACCELERATION AND GLOBAL CONVERGENCE OF A FIRST-ORDER PRIMAL-DUAL METHOD FOR NONCONVEX PROBLEMS

CLASON, Christian, Stanislav MAZURENKO a Tuomo VALKONEN

Základní údaje

Originální název

ACCELERATION AND GLOBAL CONVERGENCE OF A FIRST-ORDER PRIMAL-DUAL METHOD FOR NONCONVEX PROBLEMS

Autoři

CLASON, Christian (garant), Stanislav MAZURENKO (643 Rusko, domácí) a Tuomo VALKONEN

Vydání

SIAM JOURNAL ON OPTIMIZATION, PHILADELPHIA, SIAM PUBLICATIONS, 2019, 1052-6234

Další údaje

Jazyk

angličtina

Typ výsledku

Článek v odborném periodiku

Obor

10102 Applied mathematics

Stát vydavatele

Spojené státy

Utajení

není předmětem státního či obchodního tajemství

Odkazy

URL

Impakt faktor

Impact factor: 2.247

Kód RIV

RIV/00216224:14310/19:00113487

Organizační jednotka

Přírodovědecká fakulta

DOI

http://dx.doi.org/10.1137/18M1170194

UT WoS

000462593800036

Klíčová slova anglicky

acceleration; convergence; global; primal-dual; first order; nonconvex

Štítky

rivok

Změněno: 1. 4. 2020 22:45, Mgr. Marie Šípková, DiS.

Anotace

V originále

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.

Citovat

CLASON, Christian, Stanislav MAZURENKO a Tuomo VALKONEN. ACCELERATION AND GLOBAL CONVERGENCE OF A FIRST-ORDER PRIMAL-DUAL METHOD FOR NONCONVEX PROBLEMS. 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.

@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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