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

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14310%2F21%3A00120832" target="_blank" >RIV/00216224:14310/21:00120832 - isvavai.cz</a>

Výsledek na webu

<a href="https://doi.org/10.1007/s00245-020-09676-1" target="_blank" >https://doi.org/10.1007/s00245-020-09676-1</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/s00245-020-09676-1" target="_blank" >10.1007/s00245-020-09676-1</a>

Jazyk výsledku

angličtina

Název v původním jazyce

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

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

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

Popis výsledku anglicky

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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10102 - Applied mathematics

Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2021

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Applied Mathematics and Optimization

ISSN

0095-4616

e-ISSN

1432-0606

Svazek periodika

84

Číslo periodika v rámci svazku

2

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

46

Strana od-do

1239-1284

Kód UT WoS článku

000526189300001

EID výsledku v databázi Scopus

2-s2.0-85083766800