A Linear Separability Criterion for Sets of Euclidean Space (original) (raw)

Access this article

Log in via an institution

Subscribe and save

Buy Now

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

Instant access to the full article PDF.

References

  1. Dem’yanov, V.F.: Mathematical diagnostics via nonsmooth analysis. Optim. Methods Softw. 20(2–3), 191–212 (2005)
    Google Scholar
  2. Mangasarian, O.L.: Linear and nonlinear separation of patterns by linear programming. Oper. Res. 13(3), 444–452 (1965)
    Article MathSciNet MATH Google Scholar
  3. Bennett, K.P., Mangasarian, O.L.: Robust linear programming discrimination of two linearly inseparable sets. Optim. Methods Softw. 1, 23–34 (1992)
    Article Google Scholar
  4. Mangasarian, O.I.: Generalized Support Vector Machines. Advances in Large Margin Classifiers. MIT Press, Cambridge (2000)
    Google Scholar
  5. Gabidullina, Z.R.: On the issue of linear separability of convex polyhedra. In: “Mathematical Programming and Applications” Abstracts for Presentation at the XIV Russian Conference. UrO RAN, Yekaterinburg (2011)
    Google Scholar
  6. Gabidullina, Z.R.: A linear separability criterion for convex polyhedra. In: Book of abstracts of 25-th IFIP TC 7 Conference on System Modeling and Optimization, Berlin (2011)
    Google Scholar
  7. Gabidullina, Z.R.: A theorem on strict separability of convex polyhedra and its applications in optimization. J. Optim. Theory Appl. 148(3), 550–570 (2011)
    Article MathSciNet MATH Google Scholar
  8. Giannessi, F.: Constrained Optimization and Image Space Analysis. Volume 1. Separation of Sets and Optimality Conditions. Springer, New York (2005)
    Google Scholar
  9. Vasil’ev, F.P.: Numerical Methods for Solving Extremum Problems. Nauka, Moscow (1980)
    Google Scholar
  10. Dem’yanov, V.F., Vasil’ev, L.V.: Nondifferentiable Optimization. Nauka, Moscow (1981) (Engl. transl., Dem’yanov, V.F., Vasil’ev, L.V., Sasagawa, T., Nondifferentiable Optimization. Springer, Berlin (1985))
    MATH Google Scholar
  11. Dem’yanov, V.F., Malozemov, V.N.: Introduction to Minimax. Nauka, Moscow (1972) (Engl. transl., Dover Publications (1990))
    Google Scholar
  12. Ioffe, A.D., Tichomirov, B.M.: Theory of Extremal Problems. Nauka, Moscow (1974) (Engl. transl., Theory of Extremal Problems. Studies in Mathematics and Its Applications. Elsevier Science Ltd. (1979))
    Google Scholar
  13. Pshenichnii, B.N.: Convex Analysis and Extremal Problems. Nauka, Moscow (1980)
    Google Scholar
  14. Levitin, E.S., Polyak, B.T.: Costrained minimization methods. Ž. Vyčisl. Mat. Mat. Fiz. 6(5), 787–823 (1966)
    MATH Google Scholar
  15. Elster, K.H., Reinhart, R., Schauble, M., Donath, G.: Einführung in die Nichtlineare Optimierung. Teubner, Leipzig (1977) (Russ. transl., Introduction in Nonlinear Programming, Nauka, Moscow (1985))
    MATH Google Scholar
  16. Sukharev, A.G., Timokhov, A.V., Fedorov, V.V.: A Cource in Optimization Methods. Nauka, Moscow (1986)
    Google Scholar
  17. Konnov, I.V.: Application of the method of conjugate gradients to minimization of quasiconvex functionals. Issled. Prikl. Mat. 12, 46–58 (1984)
    MathSciNet Google Scholar
  18. Gavurin, M.K., Malozemov, V.N.: Extremum Problems with Linear Constraints. Publishing House of LGU, Leningrad (1984)
    Google Scholar
  19. Michel, M., Vaida, S.: Mathematical Programming. Theory and Algorithms. Wiley, New York (1986) (Russ. transl., Nauka, Moscow (1990))
    Google Scholar
  20. Gabidullina, Z.R.: A theorem on separability of a convex polyhedron from zero point of the space and its applications in optimization. Russ. Math. 12(12), 21–26 (2006) (Engl. transl., Russ. Math. (Iz. VUZ) 50, 18–23 (2006))
    MathSciNet Google Scholar

Download references