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Linear programming over ordered bodies

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Ukrainian Mathematical Journal Aims and scope

Abstract

The theory of linear programming over an arbitrary ordered body is considered. The Farkas and Duality Theorems are generalized. A method is given for solving the problems under consideration.

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Literature cited

  1. S. N. Chernikov. Linear Inequalities [in Russian], Nauka, Moscow (1968).

    Google Scholar 

  2. G. V. Banikov, Universal Inverse Matrices [in Russian], Deposited at VINITI, No. 951-78, Sverdlovsk (1978).

  3. G. V. Babikov, “Generalized inverse matrices and their applications in linear algebra and mathematical programming,” Communications of the Joint Institute of Nuclear Analyses, JINA, Dubna (1984).

    Google Scholar 

  4. G. V. Babikov, “Some optimization problems over rigns of matrices,” pp. 10–11, in: VII All-Union Conference, “Problems of Theoretical Cybernetics,” Thesis report, Irkutsk University, Irkutsk (1985).

    Google Scholar 

  5. G. V. Babikov, “Some problems of linear algebra and linear programming over partially ordered rings,” in: Inconsistent Optimization Models, Ural Scientific Center, Academy of Sciences of the USSR, Sverdlovsk (1987).

    Google Scholar 

  6. G. V. Babikov, “Systems of linear inequalities over partially ordered rings,” Part 2, in: Ill-Posed Models of Mathematical Programming, Deposited at BINITI, No. 2824-80, Sverdlovsk (1980).

  7. G. V. Babikov, “The use of generalized inverses of matrices in parametric programming,” in: Parametric Optimization and Ill-posed Problems in Mathematical Optimization. Semicarberocht No. 81. Humboldt-Universität, Berlin (1986).

    Google Scholar 

  8. G. V. Banikov, “Some generalizations of linear programming problems,” in: Mathematical Programming Methods and Software, thesis report, Ural Scientific Center, Academy of Sciences of the USSR, Sverdlovsk (1987).

    Google Scholar 

  9. G. V. Babikov, “Equalities and inequalities over algebraic systems,” Part 1, in: XIX All-Union Algebraic Conference, thesis report, Institute of Applied Problems of Mechanics and Mathematics of the Academy of Sciences of the Ukrainian SSR, L'vov (1987).

    Google Scholar 

  10. G. V. Babikov, “The decomposition of matrices over some universal algebras,” Dokl. Akad. Nauk SSSR,267, No. 5, 1033–1035 (1982).

    Google Scholar 

  11. G. V. Babikov, “A theorem on the decomposition of matrices and its applicants to questions of linear algebra over bodies,” in: Methods of Mathematical Programming and Their Applications, Ural Scientific Center, Academy of of Sciences of the USSR, Sverdlovsk (1979).

    Google Scholar 

  12. E. Artin, Geometric Algebra, Interscience, New York (1957).

    Google Scholar 

  13. N. V. Chernikova, “An algorithm for finding a general formula of nonnegative solutions of systems of linear inequalities,“ Zh. Vychisl. Mat. i Mat. Fiz.,5, No. 2, 334–337 (1965).

    Google Scholar 

  14. G. V. Babikov, “One approach to solving linear programming problems,” in: All-Union Conference, “Dynamic Control,” Thesis report, Ural Scientific Center of the Academy of Sciences of the USSR, Sverdlovsk (1979).

    Google Scholar 

  15. G. V. Babikov, “Factorizations of matrices and direct methods in linear algebra and linear programming,” in: Methods for Nonstationary Mathematical Programming Problems, Ural Scientific Center, Academy of Sciences of the USSR, Sverdlovsk (1979).

    Google Scholar 

  16. G. V. Babikov, “Some relations and locking into cycles in linear programming,” in: Optimization Methods and Image Recognition in Planning Problems, Sverdlovsk (1980).

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Authors and Affiliations

  1. Sverdlovsk National Economic Institute, USSR

    G. V. Babikov

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  1. G. V. Babikov
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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 42, No. 3, pp. 308–312, March, 1990.

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Babikov, G.V. Linear programming over ordered bodies. Ukr Math J 42, 274–278 (1990). https://doi.org/10.1007/BF01057008

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  • DOI: https://doi.org/10.1007/BF01057008

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