Skip to main content
SpringerLink
Log in

An interior-point method for generalized linear-fractional programming

  • Published:
Mathematical Programming Submit manuscript

Abstract

We develop an interior-point polynomial-time algorithm for a generalized linear-fractional problem. The latter problem can be regarded as a nonpolyhedral extension of the usual linear-fractional programming; typical example (which is of interest for control theory) is the minimization of the generalized eigenvalue of a pair of symmetric matrices linearly depending on the decision variables.

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. S. Boyd and L. El Ghaoui, “Method of centers for minimizing generalized eigenvalue,”Linear Algebra and Applications 188 (1993) 63–111 (Special Issue on Numerical Linear Algebra Methods in Control, Signals and Systems).

    Google Scholar 

  2. S. Boyd, L. El Ghaoui, E. Feron and V. Balakrishnan,Linear Matrix Inequalities in System and Control Science, SIAM Studies in Applied Mathematics (SIAM, Philadelphia, PA, 1994).

    Google Scholar 

  3. S. Boyd and Q. Yang, “Structured and simultaneous Lyapunov function for system stability problems,”International Journal of Control 49 (1989) 2215–2240.

    Google Scholar 

  4. R.W. Freund and F. Jarre, “An interior-point method for convex fractional programming,” AT&T Numerical Analysis Manuscript No. 93-03, Bell Laboratories, Muray Hill, NJ, 1993.

    Google Scholar 

  5. R.W. Freund and F. Jarre, “An interior-point method for multi-fractional programs with convex constraints,” AT&T Numerical Analysis Manuscript No. 93-07, Bell Laboratories, Murray Hill, NJ, 1993.

    Google Scholar 

  6. A.S. Nemirovskii, “On an algorithm of Karmarkar's type,”Izvestija AN SSSR, Tekhnitcheskaya Kibernetika 1 (1987) (in Russian).

  7. Yu. Nesterov and A. Nemirovskii,Interior-point Polynomial Algorithms in Convex Programming (SIAM, Philadelphia, PA, 1994).

    Google Scholar 

  8. M.J. Todd and B.P. Burrell, “An extension of Karmarkar's algorithm for linear programming using dual variables,”Algorithmica 1 (1986) 409–424.

    Google Scholar 

  9. Y. Ye, “On the von Neumann economic growth problem,” Working Paper Series No. 92-9, Department of Management Sciences, Univ. Iowa, Iowa City, IA, 1992.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Central Economical and Mathematical Institute, 32 Krasikova Street, 117418, Moscow, Russia

    Yu. E. Nesterov & A. S. Nemirovskii

  2. CORE, Université Catholique de Louvain, B-1348, Louvain-la-Neuve, Belgium

    Yu. E. Nesterov

  3. Industrial Engineering, Israel Institute of Technology, 3200, Technion City, Haifa, Israel

    A. S. Nemirovskii

Authors
  1. Yu. E. Nesterov
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. A. S. Nemirovskii
    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

Nesterov, Y.E., Nemirovskii, A.S. An interior-point method for generalized linear-fractional programming. Mathematical Programming 69, 177–204 (1995). https://doi.org/10.1007/BF01585557

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01585557

Keywords

Search

Navigation