Skip to main content
Log in

Boolean trends in linear inequalities

  • Published:
Journal of Applied and Industrial Mathematics Aims and scope Submit manuscript

Abstract

This is a short overview of some recent tendencies in the theory of linear inequalities that are evoked by Boolean valued analysis.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. S. S. Kutateladze, “Harpedonaptae and Abstract Convexity,” J. Appl. Indust. Math. 2(2), 215–221 (2008).

    Article  Google Scholar 

  2. Gy. Farkas, “A Fourier-féle mechanikai elv alkalmazásának algebrai alapja,” Mathematikai és Termé szettudományi Értesitö, 16, 361–364 (1898).

    Google Scholar 

  3. T. H. Kjeldsen, “Different Motivations and Goals in the Historical Development of the Theory of Systems of Linear Inequalities,” Arch. Hist. Exact Sci. 56(6), 459–538 (2002).

    Article  MathSciNet  Google Scholar 

  4. T. H. Kjeldsen, “From Measuring Tool to Geometrical Object: Minkowski’s Development of the Concept of Convex Bodies,” Arch. Hist. Exact Sci. 62(1), 59–89 (2008).

    Article  MATH  MathSciNet  Google Scholar 

  5. Encyclopedia of Optimization, Ed. by C. A. Floudas and P.M. Pardalos (Springer, New York, 2009).

    MATH  Google Scholar 

  6. J.-P. Kahane, “The Heritage of Fourier,” in Perspectives in Analysis. Essays in Honor of Lennart Carleson’s 75th Birthday (Berlin, Springer, 2005), pp. 83–95.

    Google Scholar 

  7. A. G. Kusraev and S. S. Kutateladze, Subdifferential Calculus: Theory and Applications (Nauka, Moscow, 2007) [in Russian].

    MATH  Google Scholar 

  8. A. G. Kusraev and S. S. Kutateladze, Introduction to Boolean Valued Analysis (Nauka, Moscow, 2005) [in Russian].

    MATH  Google Scholar 

  9. G. Takeuti, Two Applications of Logic to Mathematics (Iwanami Publ. & Princeton University Press, Princeton, 1978).

    MATH  Google Scholar 

  10. D. Scott, “Boolean Models and Nonstandard Analysis,” in Applications of Model Theory to Algebra, Analysis, and Probability (Holt, Rinehart, and Winston, 1969), pp. 87–92.

  11. O. L. Mangasarian, “Set Containment Characterization,” J. Glob. Optim. 24(4), 473–480 (2002).

    Article  MATH  MathSciNet  Google Scholar 

  12. M. Fiedler et al., Linear Optimization Problems with Inexact Data (Springer, New York, 2006).

    MATH  Google Scholar 

  13. P. Scowcroft, “Nonnegative Solvability of Linear Equations in Certain Ordered Rings,” Trans. Amer. Math. Soc. 358(8), 3535–3570 (2006).

    Article  MATH  MathSciNet  Google Scholar 

  14. J.-B. Lasserre, Linear and Integer Programming vs Linear Integration and Counting. A Duality Viewpoint (Springer, Dordrecht, 2009).

    Book  MATH  Google Scholar 

  15. S. S. Kutateladze, “Boolean Models and Simultaneous Inequalities,” Vladikavkaz. Math. J. 11(3), 44–50 (2009).

    MathSciNet  Google Scholar 

  16. R. Henrion, B. S. Mordukhovich, and N. M. Nam, “Second-Order Analysis of Polyhedral Systems in Finite and Infinite Dimensions With Applications to Robust Stability.” SIAM J. Optim. 20(5), 2199–2227 (2010).

    Article  MathSciNet  Google Scholar 

  17. S. S. Kutateladze, “The Farkas Lemma Revisited,” Sibirsk. Mat. Zh. 51(1), 98–109 (2010) [Siberian Math. J. 51 (1), 78–87 (2010)].

    MathSciNet  Google Scholar 

  18. A. Tarski, Logic, Semantics, Metamathematics. Papers from 1923 to 1938 (Clarendon Press, Oxford, 1956).

    Google Scholar 

  19. S. Mac Lane, “Proof, Truth, and Confusion,” Solstice 2(1), 1–21 (1991).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to S. S. Kutateladze.

Additional information

The text was submitted by the author in English.

This article bases on a talk at the opening session of the International Conference “Order Analysis and Related Problems of Mathematical Modeling,” Vladikavkaz, July 19–24, 2010, dedicated to the 10th anniversary of the Vladikavkaz Scientific Center of the Russian Academy of Sciences.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Kutateladze, S.S. Boolean trends in linear inequalities. J. Appl. Ind. Math. 4, 340–348 (2010). https://doi.org/10.1134/S1990478910030051

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S1990478910030051

Key words

Navigation