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A new look at fractional programming

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Abstract

The parametric approach to fractional programming problems is examined and a new format is proposed for it. The latter reflects the fact that the approach as a whole capitalizes on a first-order necessary and sufficient optimality condition pertaining to differentiable pseudolinear functions.

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References

  1. Jagannathan, R.,On Some Properties of Programming Problems in Parametric Form Pertaining to Fractional Programming, Management Science, Vol. 12, pp. 609–615, 1966.

    Google Scholar 

  2. Dinkelbach, W.,On Nonlinear Fractional Programming, Management Science, Vol. 13, pp. 492–498, 1967.

    Google Scholar 

  3. Schaible, S.,Fractional Programming, II: On Dinkelbach's Algorithm, Management Science, Vol. 22, pp. 868–873, 1976.

    Google Scholar 

  4. Ibaraki, T.,Solving Mathematical Programming Problems with Fractional Objective Functions, Generalized Concavity in Optimization and Economics, Edited by S. Schaible and W. T. Ziemba, Academic Press, New York, New York, pp. 441–472, 1981.

    Google Scholar 

  5. Avriel, M.,Nonlinear Programming: Analysis and Methods, Prentice-Hall, Englewood Cliffs, New Jersey, 1976.

    Google Scholar 

  6. Greenberg, H. J., andPierskalla, W. P.,A Review of Quasi-Convex Functions, Operations Research, Vol. 19, pp. 1533–1570, 1971.

    Google Scholar 

  7. Ponstein, J.,Seven Kinds of Convexity, SIAM Review, Vol. 9, pp. 115–119, 1967.

    Google Scholar 

  8. Martos, B.,The Direct Power of Adjacent Vertex Programming Methods, Management Science, Vol. 12, pp. 241–252, 1965.

    Google Scholar 

  9. Bazaraa, M. S., andShetty, C. M.,Nonlinear Programming, Theory and Algorithms, Wiley, New York, New York, 1979.

    Google Scholar 

  10. Katoh, N., andIbaraki, T.,A Parametric Characterization and an ε-Approximation Scheme for the Minimization of a Quasiconcave Program, Proceedings of the 12th International Symposium on Mathematical Programming, MIT, Cambridge, Massachusetts, 1985.

    Google Scholar 

  11. Geoffrion, A. M.,Solving Bicriterion Mathematical Programs, Operations Research, Vol. 15, pp. 39–54, 1967.

    Google Scholar 

  12. Henig, M.,The Shortest Path Problem with Two Objective Functions, European Journal of Operations Research, Vol. 25, pp. 281–291, 1986.

    Google Scholar 

  13. Kortanek, K. O., andEvans, J. P.,Pseudo-Concave Programming and Lagrange Regularity, Operations Research, Vol. 15, pp. 882–891, 1967.

    Google Scholar 

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Authors and Affiliations

  1. National Research Institute for Mathematical Sciences of the CSIR, Pretoria, South Africa

    M. Sniedovich (Senior Specialist Researcher)

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  1. M. Sniedovich
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Communicated by M. Avriel

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Sniedovich, M. A new look at fractional programming. J Optim Theory Appl 54, 113–120 (1987). https://doi.org/10.1007/BF00940407

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  • DOI: https://doi.org/10.1007/BF00940407

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