Primal-Dual Proximal Splitting and Generalized Conjugation in Non-smooth Non-convex Optimization
The result's identifiers
Result code in 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>
Result on the web
<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>
Alternative languages
Result language
angličtina
Original language name
Primal-Dual Proximal Splitting and Generalized Conjugation in Non-smooth Non-convex Optimization
Original language description
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.
Czech name
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Czech description
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Classification
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
Result continuities
Project
—
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2021
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Applied Mathematics and Optimization
ISSN
0095-4616
e-ISSN
1432-0606
Volume of the periodical
84
Issue of the periodical within the volume
2
Country of publishing house
US - UNITED STATES
Number of pages
46
Pages from-to
1239-1284
UT code for WoS article
000526189300001
EID of the result in the Scopus database
2-s2.0-85083766800