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Pseudo-duality in mathematical programs with quotients and products

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Abstract

A new approach to duality in fractional programs is described. The techniques used are based on the theory of pseudoduality. The results are generalized to include mathematical programs with quotients and products of finitely many functionals. The duals of the linear and quadratic cases are explicitly calculated, demonstrating the power of pseudo-duality theory.

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References

  1. Charnes, A., andCooper, W.,Programming with Linear Fractional Functions, Naval Research Logistics Quarterly, Vol. 9, pp. 181–196, 1962.

    Google Scholar 

  2. Schaible, S.,Analyse und Anwendungen won Quotienprogrammen, Mathematical Systems in Economics, Edited by W. Eichhorn and R. Henn, Verlag Anton Hain, Meisenheim, West Germany, 1978.

    Google Scholar 

  3. Schaible, S.,Duality in Fractional Programming: A Unified Approach, Operations Research, Vol. 24, pp. 452–461, 1976.

    Google Scholar 

  4. Passy, U., andYutav, S.,Pseudo-Duality in Mathematical Programming, part A, Unconstrained and Equality Constraints, Technion, Haifa, Israel, Operations Research, Statistics, and Economics, Mimeograph Series No. 208, 1978.

    Google Scholar 

  5. Passy, U., andYutav, S.,Pseudo-Duality Inequality Constraints: Extended Geometric Programs, Technion, Haifa, Israel, Operations Research, Statistics, and Economics, Mimeograph Series No. 210, 1978.

    Google Scholar 

  6. Passy, U., andYutav, S.,Pseudo-Duality and Saddle Points, Technion, Haifa, Israel, Operations Research, Statistics, and Economics, Mimeograph Series No. 214, 1978.

    Google Scholar 

  7. Schaible, S.,Parameter-Free Convex Equivalent and Dual Programs of Fractional Programming Problems, Zeitschrift für Operations Research, Vol. 18, pp. 187–196, 1974.

    Google Scholar 

  8. Schaible, S.,Quasi-Concave, Strictly Quasi-Concave, and Pseudo-Concave Functions, Methods of Operations Research, Edited by R. Henn, H. P. Kunzi, and H. Schubert, Verlag Anton Hain, Meisenheim, West Germany, 1972.

    Google Scholar 

  9. Passy, U.,Duality and Pseudo-Duality in Mathematical Programs with Quotients and Products of Finitely Many Functionals, Technion, Haifa, Israel, Operations Research, Statistics, and Economics, Mimeograph Series No. 218, 1978.

    Google Scholar 

  10. Klinger, A., andMangasarian, O. L.,Logarithmic Convexity and Geometric Programming, Journal of Mathematical Analysis and Applications, Vol. 24, pp. 388–408, 1968.

    Google Scholar 

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Authors and Affiliations

  1. Faculty of Industrial Engineering and Management, Technion, Haifa, Israel

    U. Passy (Professor)

Authors
  1. U. Passy
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Communicated by M. Avriel

The author wishes to thank Prof. S. Schaible for his helpful comments. In discussions with Prof. Schaible, it was found that the duals for the linear and the quadratic cases are identical with those derived in Ref. 3.

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Passy, U. Pseudo-duality in mathematical programs with quotients and products. J Optim Theory Appl 33, 349–374 (1981). https://doi.org/10.1007/BF00935249

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