Primal-Dual Proximal Splitting and Generalized Conjugation in
Non-smooth Non-convex Optimization

J 2021

Primal-Dual Proximal Splitting and Generalized Conjugation in Non-smooth Non-convex Optimization

CLASON, Christian, Stanislav MAZURENKO a Tuomo VALKONEN

Základní údaje

Originální název

Primal-Dual Proximal Splitting and Generalized Conjugation in Non-smooth Non-convex Optimization

Autoři

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

Vydání

Applied Mathematics and Optimization, New York, Springer, 2021, 0095-4616

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: 2.194

Kód RIV

RIV/00216224:14310/21:00120832

Organizační jednotka

Přírodovědecká fakulta

DOI

http://dx.doi.org/10.1007/s00245-020-09676-1

UT WoS

000526189300001

Klíčová slova anglicky

Nonsmooth optimization; Primal-dual method; Non-convex-concave saddle-points; Generalized conjugate; Potts model; Nash equilibria

Štítky

rivok

Příznaky

Mezinárodní význam, Recenzováno

Změněno: 22. 11. 2021 14:43, Mgr. Marie Šípková, DiS.

Anotace

V originále

We demonstrate that difficult non-convex non-smooth optimization problems, such as Nash equilibrium problems and anisotropic as well as isotropic Potts segmentation models, can be written in terms of generalized conjugates of convex functionals. These, in turn, can be formulated as saddle-point problems involving convex non-smooth functionals and a general smooth but non-bilinear coupling term. We then show through detailed convergence analysis that a conceptually straightforward extension of the primal-dual proximal splitting method of Chambolle and Pock is applicable to the solution of such problems. Under sufficient local strong convexity assumptions on the functionals-but still with a non-bilinear coupling term-we even demonstrate local linear convergence of the method. We illustrate these theoretical results numerically on the aforementioned example problems.

Citovat

CLASON, Christian, Stanislav MAZURENKO a Tuomo VALKONEN. Primal-Dual Proximal Splitting and Generalized Conjugation in Non-smooth Non-convex Optimization. Applied Mathematics and Optimization. New York: Springer, 2021, roč. 84, č. 2, s. 1239-1284. ISSN 0095-4616. Dostupné z: https://dx.doi.org/10.1007/s00245-020-09676-1.

@article{1700577,
   author = {Clason, Christian and Mazurenko, Stanislav and Valkonen, Tuomo},
   article_location = {New York},
   article_number = {2},
   doi = {http://dx.doi.org/10.1007/s00245-020-09676-1},
   keywords = {Nonsmooth optimization; Primal-dual method; Non-convex-concave saddle-points; Generalized conjugate; Potts model; Nash equilibria},
   language = {eng},
   issn = {0095-4616},
   journal = {Applied Mathematics and Optimization},
   title = {Primal-Dual Proximal Splitting and Generalized Conjugation in Non-smooth Non-convex Optimization},
   url = {https://doi.org/10.1007/s00245-020-09676-1},
   volume = {84},
   year = {2021}
}

TY  - JOUR
ID  - 1700577
AU  - Clason, Christian - Mazurenko, Stanislav - Valkonen, Tuomo
PY  - 2021
TI  - Primal-Dual Proximal Splitting and Generalized Conjugation in Non-smooth Non-convex Optimization
JF  - Applied Mathematics and Optimization
VL  - 84
IS  - 2
SP  - 1239-1284
EP  - 1239-1284
PB  - Springer
SN  - 00954616
KW  - Nonsmooth optimization
KW  - Primal-dual method
KW  - Non-convex-concave saddle-points
KW  - Generalized conjugate
KW  - Potts model
KW  - Nash equilibria
UR  - https://doi.org/10.1007/s00245-020-09676-1
L2  - https://doi.org/10.1007/s00245-020-09676-1
N2  - We demonstrate that difficult non-convex non-smooth optimization problems, such as Nash equilibrium problems and anisotropic as well as isotropic Potts segmentation models, can be written in terms of generalized conjugates of convex functionals. These, in turn, can be formulated as saddle-point problems involving convex non-smooth functionals and a general smooth but non-bilinear coupling term. We then show through detailed convergence analysis that a conceptually straightforward extension of the primal-dual proximal splitting method of Chambolle and Pock is applicable to the solution of such problems. Under sufficient local strong convexity assumptions on the functionals-but still with a non-bilinear coupling term-we even demonstrate local linear convergence of the method. We illustrate these theoretical results numerically on the aforementioned example problems.
ER  -

CLASON, Christian, Stanislav MAZURENKO a Tuomo VALKONEN. Primal-Dual Proximal Splitting and Generalized Conjugation in Non-smooth Non-convex Optimization. \textit{Applied Mathematics and Optimization}. New York: Springer, 2021, roč.~84, č.~2, s.~1239-1284. ISSN~0095-4616. Dostupné z: https://dx.doi.org/10.1007/s00245-020-09676-1.

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