Skip to main content
SpringerLink
Log in

Primal Newton Method for the Linear Cone Programming Problem

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

Abstract

A linear cone programming problem containing among the constraints a second-order cone is considered. For solving this problem, a primal Newton method which is constructed with the help of the optimality conditions is proposed. Local convergence of this method is proven.

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

Access this article

Log in via an institution

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. N. N. Moiseev, Elements of the Theory of Optimal Systems (Nauka, Moscow, 1975) [in Russian].

    MATH  Google Scholar 

  2. N. N. Moiseev, Yu. P. Ivanilov, and E. M. Stolyarova, Optimization Methods (Nauka, Moscow, 1978) [in Russian].

    Google Scholar 

  3. N. N. Moiseev, Selected Works, Vol. 1: Fluid Dynamics and Mechanics: Optimization, Operations Research, and Control Theory (Taideks Ko, Moscow, 2003) [in Russian].

    Google Scholar 

  4. Handbook of Semidefinite, Cone, and Polynomial Optimization: Theory, Algorithms, Software, and Applications, Ed. by M. F. Anjos and J. B. Lasserre (Springer, New York, 2011).

    Google Scholar 

  5. M. S. Lobo, L. Vandenberghe, S. Boyd, and H. Lebret, “Applications of second order cone programming,” Linear Algebra Appl. 284, 193–228 (1998).

    Article  MathSciNet  MATH  Google Scholar 

  6. Yu. E. Nesterov and M. J. Todd, “Primal-dual interior-point methods for self-scaled cones,” SIAM J. Optim. 8, 324–364 (1998).

    Article  MathSciNet  MATH  Google Scholar 

  7. R. D. C. Monteiro and T. Tsuchiya, “Polynomial convergence of primal-dual algorithms for second-order cone program based on the MZ-family of directions,” Math. Program. 88 (1), 61–83 (2000).

    Article  MathSciNet  MATH  Google Scholar 

  8. G. Pataki, “Cone-LP’s and semidefinite programs: Geometry and simplex-type method, integer programming and combinatorial optimization,” Lecture Notes Comput. Sci. 1084, 162–174 (1996).

    Article  MathSciNet  Google Scholar 

  9. M. Muramatsu, “A pivoting procedure for a class of second-order cone programming,” Optim. Methods Software 21 (2), 295–314 (2006).

    Article  MathSciNet  MATH  Google Scholar 

  10. Sh. Hayashi, T. Okuno, and Y. Ito, “Simplex-type algorithm for second-order cone programming via semiinfinite programming reformulation,” Optim. Methods Software 31 (6), 1272–1297 (2016).

    Article  MathSciNet  MATH  Google Scholar 

  11. V. G. Zhadan, “Primal Newton method for linear semidefinite programming problems,” Tr. Inst. Mat. Mekh. Ural. Otd. Ross. Akad. Nauk 14 (2), 67–80 (2008).

    Google Scholar 

  12. F. Alizadeh and D. Goldfarb, “Second-order cone programming,” Math. Program., Ser. B 95, 3–51 (2003).

    Article  MathSciNet  MATH  Google Scholar 

  13. J. Ortega and W. Rheinboldt, Iterative Solution of Nonlinear Equations of Several Variables (McGraw-Hill, New York, 1970).

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Dorodnitsyn Computing Center, FRC “Computer Science and Control” of RAS, Moscow, 119333, Russia

    V. G. Zhadan

Authors
  1. V. G. Zhadan
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to V. G. Zhadan.

Additional information

Dedicated to the 100th birthday of Academician N.N. Moiseev

Original Russian Text © V.G. Zhadan, 2018, published in Zhurnal Vychislitel’noi Matematiki i Matematicheskoi Fiziki, 2018, Vol. 58, No. 2, pp. 220–227.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Zhadan, V.G. Primal Newton Method for the Linear Cone Programming Problem. Comput. Math. and Math. Phys. 58, 207–214 (2018). https://doi.org/10.1134/S0965542518020173

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0965542518020173

Keywords

Search

Navigation