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

Result code in 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>
Result on the web
<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>

Result language
angličtina
Original language name
Primal-dual block-proximal splitting for a class of non-convex problems
Original language description
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.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10102 - Applied mathematics

Project
<a href="/en/project/EF17_050%2F0008496" target="_blank" >EF17_050/0008496: MSCAfellow@MUNI</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2020
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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