Primal-dual block-proximal splitting for a class of non-convex
problems

J 2020

Primal-dual block-proximal splitting for a class of non-convex problems

MAZURENKO, Stanislav; Jyrki JAUHIAINEN and Tuomo VALKONEN

Basic information

Original name

Primal-dual block-proximal splitting for a class of non-convex problems

Authors

MAZURENKO, Stanislav (643 Russian Federation, guarantor, belonging to the institution); Jyrki JAUHIAINEN and Tuomo VALKONEN

Edition

Electronic Transactions on Numerical Analysis, Kent, Kent State University, 2020, 1068-9613

Other information

Language

English

Type of outcome

Article in a journal

Field of Study

10102 Applied mathematics

Country of publisher

United States of America

Confidentiality degree

is not subject to a state or trade secret

References:

URL

Impact factor

Impact factor: 0.959

RIV identification code

RIV/00216224:14310/20:00118171

Organization unit

Faculty of Science

DOI

http://dx.doi.org/10.1553/etna_vol52s509

UT WoS

000592187100027

EID Scopus

2-s2.0-85092726928

Keywords in English

primal-dual algorithms; convex optimization; non-smooth optimization; step length

Abstract

In the original language

We develop block structure-adapted primal-dual algorithms for non-convex non-smooth optimisation problems, whose objectives can be written as compositions G(x) + F(K(x)) of non-smooth block-separable convex functions G and F with a nonlinear Lipschitz-differentiable operator K. Our methods are refinements of the nonlinear primal-dual proximal splitting method for such problems without the block structure, which itself is based on the primal-dual proximal splitting method of Chambolle and Pock for convex problems. We propose individual step length parameters and acceleration rules for each of the primal and dual blocks of the problem. This allows them to convergence faster by adapting to the structure of the problem. For the squared distance of the iterates to a critical point, we show local O(1/N), O(1/N-2), and linear rates under varying conditions and choices of the step length parameters. Finally, we demonstrate the performance of the methods for the practical inverse problems of diffusion tensor imaging and electrical impedance tomography.

Links

EF17_050/0008496, research and development project

Name: MSCAfellow@MUNI

Cite

MAZURENKO, Stanislav; Jyrki JAUHIAINEN and Tuomo VALKONEN. Primal-dual block-proximal splitting for a class of non-convex problems. Electronic Transactions on Numerical Analysis. Kent: Kent State University, 2020, vol. 52, No 2020, p. 509-552. ISSN 1068-9613. Available from: https://dx.doi.org/10.1553/etna_vol52s509.

@article{1742276,
   author = {Mazurenko, Stanislav and Jauhiainen, Jyrki and Valkonen, Tuomo},
   article_location = {Kent},
   article_number = {2020},
   doi = {http://dx.doi.org/10.1553/etna_vol52s509},
   keywords = {primal-dual algorithms; convex optimization; non-smooth optimization; step length},
   language = {eng},
   issn = {1068-9613},
   journal = {Electronic Transactions on Numerical Analysis},
   title = {Primal-dual block-proximal splitting for a class of non-convex problems},
   url = {https://epub.oeaw.ac.at/?arp=0x003bd91d},
   volume = {52},
   year = {2020}
}

TY  - JOUR
ID  - 1742276
AU  - Mazurenko, Stanislav - Jauhiainen, Jyrki - Valkonen, Tuomo
PY  - 2020
TI  - Primal-dual block-proximal splitting for a class of non-convex problems
JF  - Electronic Transactions on Numerical Analysis
VL  - 52
IS  - 2020
SP  - 509-552
EP  - 509-552
PB  - Kent State University
SN  - 10689613
KW  - primal-dual algorithms
KW  - convex optimization
KW  - non-smooth optimization
KW  - step length
UR  - https://epub.oeaw.ac.at/?arp=0x003bd91d
L2  - https://epub.oeaw.ac.at/?arp=0x003bd91d
N2  - We develop block structure-adapted primal-dual algorithms for non-convex non-smooth optimisation problems, whose objectives can be written as compositions G(x) + F(K(x)) of non-smooth block-separable convex functions G and F with a nonlinear Lipschitz-differentiable operator K. Our methods are refinements of the nonlinear primal-dual proximal splitting method for such problems without the block structure, which itself is based on the primal-dual proximal splitting method of Chambolle and Pock for convex problems. We propose individual step length parameters and acceleration rules for each of the primal and dual blocks of the problem. This allows them to convergence faster by adapting to the structure of the problem. For the squared distance of the iterates to a critical point, we show local O(1/N), O(1/N-2), and linear rates under varying conditions and choices of the step length parameters. Finally, we demonstrate the performance of the methods for the practical inverse problems of diffusion tensor imaging and electrical impedance tomography.
ER  -

MAZURENKO, Stanislav; Jyrki JAUHIAINEN and Tuomo VALKONEN. Primal-dual block-proximal splitting for a class of non-convex problems. \textit{Electronic Transactions on Numerical Analysis}. Kent: Kent State University, 2020, vol.~52, No~2020, p.~509-552. ISSN~1068-9613. Available from: https://dx.doi.org/10.1553/etna\_{}vol52s509.

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