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Zh. Vychisl. Mat. Mat. Fiz., 2009, Volume 49, Number 12, Pages 2114–2130 (Mi zvmmf4793)  

This article is cited in 9 scientific papers (total in 9 papers)

On a class of interior point algorithms

V. I. Zorkal'tsev

Melent’ev Institute of Power Engineering Systems, Siberian Branch, Russian Academy of Sciences, ul. Lermontova 130, Irkutsk, 664033, Russia

Abstract: A family of interior point algorithms for solving linear programs is examined. Under the assumption on the nondegeneracy of the problem, a theoretical justification of these algorithms is given. The sets of the algorithms converging to relatively interior optimal solutions and having linear or superlinear convergence rate are identified.

Key words: linear programming, interior point method, linear and superlinear convergence of interior point algorithms.

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English version:
Computational Mathematics and Mathematical Physics, 2009, 49:12, 2017–2033

Bibliographic databases:

UDC: 519.626
Received: 16.02.2009
Revised: 24.06.2009

Citation: V. I. Zorkal'tsev, “On a class of interior point algorithms”, Zh. Vychisl. Mat. Mat. Fiz., 49:12 (2009), 2114–2130; Comput. Math. Math. Phys., 49:12 (2009), 2017–2033

Citation in format AMSBIB
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\paper On a~class of interior point algorithms
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\pages 2114--2130
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\jour Comput. Math. Math. Phys.
\yr 2009
\vol 49
\issue 12
\pages 2017--2033
\crossref{https://doi.org/10.1134/S0965542509120033}
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. V. I. Zorkaltsev, “Dual interior point algorithms”, Russian Math. (Iz. VUZ), 55:4 (2011), 26–43  mathnet  crossref  mathscinet
    2. V. G. Zhadan, A. A. Orlov, “O skhodimosti dvoistvennogo metoda Nyutona dlya lineinoi zadachi poluopredelennogo programmirovaniya”, Izvestiya Irkutskogo gosudarstvennogo universiteta. Seriya Matematika, 4:2 (2011), 75–90  mathnet
    3. V. I. Zorkaltsev, S. M. Perzhabinskii, “Modeli otsenki defitsita moschnosti elektroenergeticheskoi sistemy”, Sib. zhurn. industr. matem., 15:1 (2012), 34–43  mathnet  mathscinet
    4. V. I. Zorkaltsev, D. S. Medvezhonkov, “Chislennye eksperimenty s variantami algoritmov vnutrennikh tochek na nelineinykh zadachakh potokoraspredeleniya”, UBS, 46 (2013), 68–87  mathnet
    5. Medvezhonkov D.S., “Eksperimentalnye issledovaniya algoritmov vnutrennikh tochek na nelineinykh zadachakh potokoraspredeleniya”, Vestnik Buryatskogo gosudarstvennogo universiteta, 2013, no. 9, 12–16  elib
    6. Zorkaltsev V.I., Perzhabinskii S.M., “Algoritmy vnutrennikh tochek v lineinom i nelineinom programmirovanii”, Omskii nauchnyi vestnik, 2013, no. 1(117), 25–28  mathscinet  elib
    7. V. I. Zorkaltsev, “The search for admissible solutions by the interior point algorithms”, Num. Anal. Appl., 9:3 (2016), 191–206  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    8. V. I. Zorkaltsev, I. V. Mokryi, “Interior point algorithms in linear optimization”, J. Appl. Industr. Math., 12:1 (2018), 191–199  mathnet  crossref  crossref  elib
    9. V. I. Zorkal'tsev, “Octahedral projections of a point onto a polyhedron”, Comput. Math. Math. Phys., 58:5 (2018), 813–821  mathnet  crossref  crossref  isi  elib
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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