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

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

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

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

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

Popis výsledku anglicky

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.

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

2019

Kód důvěrnosti údajů

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

Název periodika

SIAM JOURNAL ON OPTIMIZATION

ISSN

1052-6234

e-ISSN

—

Svazek periodika

29

Číslo periodika v rámci svazku

1

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

31

Strana od-do

933-963

Kód UT WoS článku

000462593800036

EID výsledku v databázi Scopus

2-s2.0-85065421654