On Coordinate-Wise Minimization Applied to General Convex Optimization Problems
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21230%2F20%3A00343072" target="_blank" >RIV/68407700:21230/20:00343072 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1016/j.procs.2020.09.142" target="_blank" >https://doi.org/10.1016/j.procs.2020.09.142</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.procs.2020.09.142" target="_blank" >10.1016/j.procs.2020.09.142</a>
Alternative languages
Result language
angličtina
Original language name
On Coordinate-Wise Minimization Applied to General Convex Optimization Problems
Original language description
In this paper, we theoretically analyze principal properties of coordinate-wise minimization and we answer a few open questions related to it. In particular, we show that for minimizing any differentiable convex function on a given convex polyhedron, there exists a finite set of directions determined only by the polyhedron such that any local minimum with respect to these directions is a global minimum. We prove that the set of directions has a `nice’ structure for polyhedra defined by a k-regular matrix, which is a generalization of total unimodularity. We proceed to show that for some simple polyhedra, the number of these directions is polynomial, which subsumes already existing algorithms. We prove that the main result can not be extended for the case when the polyhedron is not known in advance or if the optimization is performed over a general convex set.
Czech name
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Czech description
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Classification
Type
D - Article in proceedings
CEP classification
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OECD FORD branch
10100 - Mathematics
Result continuities
Project
<a href="/en/project/GA19-09967S" target="_blank" >GA19-09967S: Compositional Architectures for Pattern Recognition</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2020
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Article name in the collection
Knowledge-Based and Intelligent Information & Engineering Systems: Proceedings of the 24th International Conference KES2020
ISBN
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ISSN
1877-0509
e-ISSN
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Number of pages
10
Pages from-to
1328-1337
Publisher name
Elsevier B.V.
Place of publication
Amsterdam
Event location
Verona
Event date
Sep 16, 2020
Type of event by nationality
WRD - Celosvětová akce
UT code for WoS article
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