Skip to main content
SpringerLink
Log in

Convergence of a Dual-Variable Vector Sequence in a Semi-Definite Programming Problem

  • Published:
Cybernetics and Systems Analysis Aims and scope

Abstract

An iterative algorithm is proposed in the paper for determination of a feasible solution to a linear semi-definite programming problem. A basic result of convergence of the interior point method is proved. Two strategies of choosing a step value are considered.

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.

Institutional subscriptions

Similar content being viewed by others

REFERENCES

  1. P. Gahinet and A. Nemirovski, “The projective method for solving linear matrix inequalities,” Math. Progr., 77, No. 2, 163-190 (1997).

    Google Scholar 

  2. I. I. Dikin, “Determining the interior point of a system of linear inequalities,” Kibern. Sist. Analiz, No. 1, 67-74 (1992).

  3. I. I. Dikin, “Determining the interior admissible point of a system of linear constraints,” Kibern. Sist. Analiz, No. 5, 152-164 (1997).

  4. B. N. Pshenichnyi and E. I. Nenakhov, “Matrix problems of mathematical programming,” Kibern. Sist. Analiz, No. 2, 120-131 (1996).

  5. C. Roos, “On Karmarkar's projective method for linear programming,” in: Report No. 85-23, Delft University of Technology (1985).

  6. I. I. Dikin, Definition of Admissible and Optimal Solutions by the Method of Interior Points [in Russian], Nauka, Sib. Predpr. RAN, Novosibirsk (1998).

    Google Scholar 

  7. I. I. Dikin and C. Roos, “Convergence of the dual variables for the primal affine scaling method with unit steps in the homogeneous case,” J. Optimiz. Theory Appl., 95, No. 2, 305-321 (1997).

    Google Scholar 

  8. T. Tsuchiya and M. Muramatsu, “Global convergence of a long-step affine scaling algorithm for degenerate linear programming problems,” SIAM J. Optimiz., 5, No. 3, 525-551 (1995).

    Google Scholar 

  9. R. Saigal, Linear Programming: A Modern Integrated Analysis, Kluwer Acad. Publ., Dordrecht (1995).

    Google Scholar 

  10. I. I. Dikin and O. M. Popova, Analysis and Acceleration of Convergence of the Algorithms of the Method of Interior Points: Solution of Optimization Problems of Thermodynamics [in Russian], Nauka, Sib. Predpr. RAN, Novosibirsk (1997).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Siberian Department of the Russian Academy of Sciences, L. A. Melent'ev Institute of Energetic Systems, Irkutsk, Russia

    I. I. Dikin

Authors
  1. I. I. Dikin
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Dikin, I.I. Convergence of a Dual-Variable Vector Sequence in a Semi-Definite Programming Problem. Cybernetics and Systems Analysis 39, 298–304 (2003). https://doi.org/10.1023/A:1024751609167

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1024751609167

Search

Navigation