Trudy Instituta Matematiki i Mekhaniki UrO RAN
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Archive
Impact factor

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Trudy Inst. Mat. i Mekh. UrO RAN:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2023, Volume 29, Number 3, Pages 73–87
DOI: https://doi.org/10.21538/0134-4889-2023-29-3-73-87
(Mi timm2019)
 

A Bicomposition of Conical Projections

E. A. Nurminski

Far Eastern Federal University, Vladivostok
References:
Abstract: We consider a decomposition approach to the problem of finding the orthogonal projection of a given point onto a convex polyhedral cone represented by a finite set of its generators. The reducibility of an arbitrary linear optimization problem to such projection problem potentially makes this approach one of the possible new ways to solve large-scale linear programming problems. Such an approach can be based on the idea of a recurrent dichotomy that splits the original large-scale problem into a binary tree of conical projections corresponding to a successive decomposition of the initial cone into the sum of lesser subcones. The key operation of this approach consists in solving the problem of projecting a certain point onto a cone represented as the sum of two subcones with the smallest possible modification of these subcones and their arbitrary selection. Three iterative algorithms implementing this basic operation are proposed, their convergence is proved, and numerical experiments demonstrating both the computational efficiency of the algorithms and certain challenges in their application are performed.
Keywords: orthogonal projection, polyhedral cones, decomposition, linear optimization.
Funding agency Grant number
Ministry of Science and Higher Education of the Russian Federation 075-02-2023-946
This work was carried out at the Far-East Mathematical Research Center and was supported by the Ministry of Science and Higher Education of the Russian Federation (agreement no. 075-02-2023-946 of February 16, 2023, for the realization of programs for the development of regional centers for mathematical research and education).
Received: 25.05.2023
Revised: 08.07.2023
Accepted: 17.07.2023
English version:
Proceedings of the Steklov Institute of Mathematics (Supplementary issues), 2023, Volume 323, Issue 1, Pages S179–S193
DOI: https://doi.org/10.1134/S0081543823060160
Bibliographic databases:
Document Type: Article
UDC: 519.85
MSC: 47H09, 90C25, 90C06
Language: Russian
Citation: E. A. Nurminski, “A Bicomposition of Conical Projections”, Trudy Inst. Mat. i Mekh. UrO RAN, 29, no. 3, 2023, 73–87; Proc. Steklov Inst. Math. (Suppl.), 323, suppl. 1 (2023), S179–S193
Citation in format AMSBIB
\Bibitem{Nur23}
\by E.~A.~Nurminski
\paper A Bicomposition of Conical Projections
\serial Trudy Inst. Mat. i Mekh. UrO RAN
\yr 2023
\vol 29
\issue 3
\pages 73--87
\mathnet{http://mi.mathnet.ru/timm2019}
\crossref{https://doi.org/10.21538/0134-4889-2023-29-3-73-87}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4649593}
\elib{https://elibrary.ru/item.asp?id=54393168}
\edn{https://elibrary.ru/lkcnez}
\transl
\jour Proc. Steklov Inst. Math. (Suppl.)
\yr 2023
\vol 323
\issue , suppl. 1
\pages S179--S193
\crossref{https://doi.org/10.1134/S0081543823060160}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85185145350}
Linking options:
  • https://www.mathnet.ru/eng/timm2019
  • https://www.mathnet.ru/eng/timm/v29/i3/p73
  • Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Trudy Instituta Matematiki i Mekhaniki UrO RAN
     
      Contact us:
     Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2024