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Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2013, Volume 19, Number 2, Pages 98–108 (Mi timm936)  
This article is cited in 4 scientific papers (total in 4 papers)

Generalized Newton method for linear optimization problems with inequality constraints

A. I. Golikov, Yu. G. Evtushenko

Dorodnitsyn Computing Centre of the Russian Academy of Sciences
Full-text PDF (202 kB) Citations (4)
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Abstract: A dual problem of linear programming (LP) is reduced to the unconstrained maximization of a concave piecewise quadratic function for sufficiently large values of a certain parameter. An estimate is given for the threshold value of the parameter starting from which the projection of a given point on the set of solutions of the dual LP problem in dual and auxiliary variables is easily found by means of a single solution of an unconstrained maximization problem. The unconstrained maximization is carried out by the generalized Newton method, which is globally convergent in a finite number of steps. The results of numerical experiments are presented for randomly generated large-scale LP problems.
Keywords: linear programming problem, piecewise quadratic function, unconstrained maximization, generalized Newton method.
Received: 11.02.2013
English version:
Proceedings of the Steklov Institute of Mathematics (Supplementary issues), 2014, Volume 284, Issue 1, Pages 96–107
DOI: https://doi.org/10.1134/S0081543814020096
Bibliographic databases:
Document Type: Article
UDC: 519.854
Language: Russian
Citation: A. I. Golikov, Yu. G. Evtushenko, “Generalized Newton method for linear optimization problems with inequality constraints”, Trudy Inst. Mat. i Mekh. UrO RAN, 19, no. 2, 2013, 98–108; Proc. Steklov Inst. Math. (Suppl.), 284, suppl. 1 (2014), 96–107
Citation in format AMSBIB
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  • https://www.mathnet.ru/eng/timm/v19/i2/p98
    • This publication is cited in the following 4 articles:
    1. R.V. Namm, G.I. Tsoy, “Solution of the static contact problem with Coulomb friction between an elastic body and a rigid foundation”, Journal of Computational and Applied Mathematics, 419 (2023), 114725  crossref
    2. V. I. Zabotin, Yu. A. Chernyaev, “Newton's method for minimizing a convex twice differentiable function on a preconvex set”, Comput. Math. Math. Phys., 58:3 (2018), 322–327  mathnet  crossref  crossref  isi  elib
    3. G. A. Amirkhanova, A. I. Golikov, Yu. G. Evtushenko, “On an inverse linear programming problem”, Proc. Steklov Inst. Math. (Suppl.), 295, suppl. 1 (2016), 21–27  mathnet  crossref  mathscinet  isi  elib
    4. A. I. Golikov, Yu. G. Evtushenko, “Regularization and normal solutions of systems of linear equations and inequalities”, Proc. Steklov Inst. Math. (Suppl.), 289, suppl. 1 (2015), 102–110  mathnet  crossref  mathscinet  isi  elib
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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