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Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2012, Volume 18, Number 3, Pages 83–89 (Mi timm841)  
This article is cited in 4 scientific papers (total in 5 papers)

Interior penalty functions and duality in linear programming

I. I. Eremina, L. D. Popovab

a Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences
b Ural Federal University
Full-text PDF (148 kB) Citations (5)
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Abstract: Logarithmic additive terms of barrier type with a penalty parameter are included into the Lagrange function of a linear programming problem. As a result, the problem of searching for saddle points of the modified Lagrangian becomes unconstrained (the saddle point is sought with respect to the whole space of primal and dual variables). Theorems on the asymptotic convergence to the desired solution and analogs of the duality theorems for the arising optimization minimax and maximin problem statements are formulated.
Keywords: linear programming, uality, inner penalty functions.
Received: 25.02.2012
English version:
Proceedings of the Steklov Institute of Mathematics (Supplementary issues), 2013, Volume 283, Issue 1, Pages 56–63
DOI: https://doi.org/10.1134/S0081543813090058
Bibliographic databases:
Document Type: Article
UDC: 519.658.4
Language: Russian
Citation: I. I. Eremin, L. D. Popov, “Interior penalty functions and duality in linear programming”, Trudy Inst. Mat. i Mekh. UrO RAN, 18, no. 3, 2012, 83–89; Proc. Steklov Inst. Math. (Suppl.), 283, suppl. 1 (2013), 56–63
Citation in format AMSBIB
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  • https://www.mathnet.ru/eng/timm841
  • https://www.mathnet.ru/eng/timm/v18/i3/p83
    • This publication is cited in the following 5 articles:
    1. L. D. Popov, “Barery i simmetrichnaya regulyarizatsiya funktsii Lagranzha pri analize nesobstvennykh zadach lineinogo programmirovaniya”, Tr. IMM UrO RAN, 29, no. 3, 2023, 138–155  mathnet  crossref  mathscinet  elib
    2. V. I. Erokhin, “O nekotorykh dostatochnykh usloviyakh razreshimosti i nerazreshimosti zadach matrichnoi korrektsii nesobstvennykh zadach lineinogo programmirovaniya”, Tr. IMM UrO RAN, 21, no. 3, 2015, 110–116  mathnet  mathscinet  elib
    3. L. D. Popov, “Dual approach to the application of barrier functions for the optimal correction of improper linear programming problems of the first kind”, Proc. Steklov Inst. Math. (Suppl.), 288, suppl. 1 (2015), 173–179  mathnet  crossref  mathscinet  isi  elib
    4. V. I. Berdyshev, V. V. Vasin, S. V. Matveev, A. A. Makhnev, Yu. N. Subbotin, N. N. Subbotina, V. N. Ushakov, M. Yu. Khachai, A. G. Chentsov, “Ivan Ivanovich Eremin”, Proc. Steklov Inst. Math. (Suppl.), 289, suppl. 1 (2015), 1–8  mathnet  crossref  mathscinet  isi  elib
    5. A. I. Golikov, Yu. G. Evtushenko, “Generalized Newton method for linear optimization problems with inequality constraints”, Proc. Steklov Inst. Math. (Suppl.), 284, suppl. 1 (2014), 96–107  mathnet  crossref  mathscinet  isi  elib
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