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Journal of Global Optimization

, Volume 6, Issue 2, pp 179–191 | Cite as

Efficient algorithms for solving certain nonconvex programs dealing with the product of two affine fractional functions

  • Le D. Muu
  • Bui T. Tam
  • S. Schaible
Article

Abstract

Two algorithms for finding a global minimum of the product of two affine fractional functions over a compact convex set and solving linear fractional programs with an additional constraint defined by the product of two affine fractional functions are proposed. The algorithms are based on branch and bound techniques using an adaptive branching operation which takes place in one-dimensional intervals. Results from numerical experiments show that large scale problems can be efficiently solved by the proposed methods.

Key words

Product of two fractional functions global optimization branch and bound adaptive branching efficiency 

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References

  1. 1.
    Charnes, A. and Cooper, W. W. (1962), Programming with Linear Fractional Functionals,Naval Research Logistics Quarterly 9, 181–186.Google Scholar
  2. 2.
    Falk, J. E. and Palocsay, S. W. (1994), Image Space Analysis of Generalized Fractional Programs,J. of Global Optimization 4, 63–88.Google Scholar
  3. 3.
    Horst, R. and Tuy, H. (1993),Global Optimization: Deterministic Approaches. Springer-Verlag, Berlin.Google Scholar
  4. 4.
    Konno, H. and Inori, M. (1988), Bond Portfolio Optimization by Bilinear Fractional Programming,Journal Operations Research Society of Japan 32, 143–158.Google Scholar
  5. 5.
    Konno, H. and Yajima, Y. (1992), Minimizing and Maximizing the Product of Linear Fractional Functions, eds. C. Floudas and M. Pardalos,Recent Advances in Global Optimization, 259–273.Google Scholar
  6. 6.
    Konno, H., Yajima, Y. and Matsui, T. (1991), Parametric Simplex Algorithms for Solving a Special Class of Nonconvex Minimization Problems,Journal of Global Optimization 1, 65–81.Google Scholar
  7. 7.
    Kuno, T., Konno, H. and Yamamoto, Y. (1992), A Parametric Successive Underestimation Method for Convex Programming Problems with an Additional Convex Multiplicative Constraint,Journal Operations Research Society of Japan 35, 290–299.Google Scholar
  8. 8.
    Muu, Le D. and Oettli, W. (1991), A Method for Minimizing a Convex-Concave Function over a Convex Set,Journal of Optimization Theory and Applications 70, 337–384.Google Scholar
  9. 9.
    Muu, Le D. and Tam, B. T. (1992), Minimizing the Sum of a Convex Function and the Product of Two Affine Functions over a Convex Set,Optimization 24, 57–62.Google Scholar
  10. 10.
    Pardalos, P. M. (1990), Polynomial Time Algorithms for Some Classes of Constrained Nonconvex Quadratic Problems,Optimization 21, 843–853.Google Scholar
  11. 11.
    Thach, P. T., Burkard, R. E., and Oettli, W. (1991), Mathematical Programs with a Two-Dimensional Reverse Convex Constraint,Journal of Global Optimization 2, 145–154.Google Scholar
  12. 12.
    Tu, P. N. V. (1984),Introductory Optimization Dynamics, Springer-Verlag, Berlin.Google Scholar
  13. 13.
    Tuy, H. (1990), Polyhedral Annexation, Dualization and Dimension Reduction Technique in Global Optimization, preprint the Linköping Institute of Technology.Google Scholar
  14. 14.
    Tuy, H. and Tam, B. T. (1992), An Efficient Solution Method for Rank Two Quasi-Concave Minimization Problems,Optimization 24, 43–56.Google Scholar

Copyright information

© Kluwer Academic Publishers 1995

Authors and Affiliations

  • Le D. Muu
    • 1
  • Bui T. Tam
    • 1
  • S. Schaible
    • 2
  1. 1.Institute of MathematicsHanoiVietnam
  2. 2.Graduate School of ManagementUniversity of CaliforniaRiversideUSA

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