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

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14310%2F20%3A00118171" target="_blank" >RIV/00216224:14310/20:00118171 - isvavai.cz</a>

Výsledek na webu

<a href="https://epub.oeaw.ac.at/?arp=0x003bd91d" target="_blank" >https://epub.oeaw.ac.at/?arp=0x003bd91d</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1553/etna_vol52s509" target="_blank" >10.1553/etna_vol52s509</a>

Jazyk výsledku

angličtina

Název v původním jazyce

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

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

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

Popis výsledku anglicky

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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10102 - Applied mathematics

Projekt

<a href="/cs/project/EF17_050%2F0008496" target="_blank" >EF17_050/0008496: MSCAfellow@MUNI</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2020

Kód důvěrnosti údajů

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

Název periodika

Electronic Transactions on Numerical Analysis

ISSN

1068-9613

e-ISSN

—

Svazek periodika

52

Číslo periodika v rámci svazku

2020

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

44

Strana od-do

509-552

Kód UT WoS článku

000592187100027

EID výsledku v databázi Scopus

2-s2.0-85092726928