Skip to main content
Log in

New modifications of the generalized saddle version of the level method

  • Published:
Computational Mathematics and Mathematical Physics Aims and scope Submit manuscript

Abstract

New modifications are proposed for the iterative method that seeks a saddle point of a convex-concave function whose efficient set is contained in the Cartesian product of polyhedra. The convergence rate of these modifications is estimated.

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.

Similar content being viewed by others

References

  1. K. Ber, E. G. Gol’shtein, and N. A. Sokolov, “Method for Finding a Saddle Point of Function Whose Domain Is Contained in Polyhedron,” Ekon. Mat. Metody 37(3), 97–105 (2001).

    Google Scholar 

  2. E. G. Gol’shtein, “Generalized Saddle Version of the Level Method,” Zh. Vychisl. Mat. Mat. Fiz. 41, 1139–1147 (2001) [Comput. Math. Math. Phys. 41, 1083–1091 (2001)].

    MathSciNet  Google Scholar 

  3. C. Lemaréchal, A. Nemirovskii, and Yu. Nesterov, “New Variants of Bundle Methods,” Math. Program. 69, 111–147 (1995).

    Article  Google Scholar 

  4. E. G. Gol’shtein, A. S. Nemirovskii, and Yu. E. Nesterov, “The Level Method, Its Generalization and Applications,” Ekon. Mat. Metody 31(3), 164–180 (1995).

    Google Scholar 

  5. N. A. Sokolov, “New Variants of the Generalized Level Method for Minimization of Convex Nondifferentiable Functions Taking Infinite Values,” Zh. Vychisl. Mat. Mat. Fiz. 48, 2037–2054 (2007) [Comput. Math. Math. Phys. 48, 1952–1969 (2007)].

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to N. A. Sokolov.

Additional information

Original Russian Text © N.A. Sokolov, 2009, published in Zhurnal Vychislitel’noi Matematiki i Matematicheskoi Fiziki, 2009, Vol. 49, No. 1, pp. 26–50.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Sokolov, N.A. New modifications of the generalized saddle version of the level method. Comput. Math. and Math. Phys. 49, 23–46 (2009). https://doi.org/10.1134/S0965542509010035

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0965542509010035

Keywords

Navigation