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Modified Ratio Objective Approach in Mathematical Programming

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Abstract

A new approach to obtaining the optimality conditions for fractional mathematical programming problems involving one objective ratio in the objective function is considered. Using this approach, an equivalent optimization problem is constructed by a modification of the single-ratio objective function in the fractional programming problem. Furthermore, an η-Lagrange function is introduced for a constructed optimization problem and modified saddle-point results are presented.

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References

  1. S. Schaible (1982) ArticleTitleBibliography in Fractional Programming Zeitschrift für Operations Research. 26 211–241

    Google Scholar 

  2. I.M.. Stancu-Minasian (1992) ArticleTitleA Fourth Bibliography of Fractional Programming Optimization. 23 53–71

    Google Scholar 

  3. C.R. Bector S. Chandra M.K. Bector (1989) ArticleTitleGeneralized Fractional Programming Duality: Parametric Approach Journal of Optimization Theory and Applications. 60 243–260 Occurrence Handle10.1007/BF00940006

    Article  Google Scholar 

  4. V. Jeyakumar B. Mond (1999) ArticleTitleOn Generalized Convex Mathematical Programming Journal of the Australian Mathematical Society. 34B 43–53

    Google Scholar 

  5. R. Jagannathan (1973) ArticleTitleDuality for Nonlinear Fractional Programs Zeitschrift für Operations Research. 17 1–3

    Google Scholar 

  6. Z.A. Khan M.A.. Hanson (1997) ArticleTitleOn Ratio Invexity in Mathematical Programming Journal of Mathematical Analysis and Applications. 205 330–336 Occurrence Handle10.1006/jmaa.1997.5180

    Article  Google Scholar 

  7. Schaible, S.. (1973). Fractional Programming: Transformations, Duality, and Algorithmic Aspects. Technical Report 73–9, Department of Operations Research, Stanford University.

  8. S. Schaible (1978) Analyse and Anwendungen von Quotientenprogrammen Hain Verlag. Meisenheim Germany.

    Google Scholar 

  9. M.A.. Hanson (1999) ArticleTitleOn Sufficiency of the Kuhn-Tucker Conditions Journal of Mathematical Analysis and Applications. 80 545–550 Occurrence Handle10.1016/0022-247X(81)90123-2

    Article  Google Scholar 

  10. A. Ben-Israel B. Mond (1986) ArticleTitleWhat Is Invexity? Journal of the Australian Mathematical Society. 28 1–9

    Google Scholar 

  11. B.D. Craven (1981) ArticleTitleInvex Functions and Constrained Local Minima Bulletin of the Australian Mathematical Society. 24 357–366

    Google Scholar 

  12. R.R. Egudo M.A. Hanson (1987) ArticleTitleMultiobjective Duality with Invexity Journal of Mathematical Analysis and Applications. 126 469–477 Occurrence Handle10.1016/0022-247X(87)90054-0

    Article  Google Scholar 

  13. R. Pini (1991) ArticleTitleInvexity and Generalized Convexity Optimization. 22 513–525

    Google Scholar 

  14. T. Antczak (2003) ArticleTitleA New Approach to Multiobjective Programming with a Modified Objective Function Journal of Global Optimization. 27 485–495 Occurrence Handle10.1023/A:1026080604790

    Article  Google Scholar 

  15. M.S. Bazaraa H.D. Sherali C.M.. Shetty (1991) Nonlinear Programming: Theory and Algorithms John Wiley and Sons New York, NY

    Google Scholar 

  16. O.L. Mangasarian (1969) Nonlinear Programming McGraw-Hill New York, NY.

    Google Scholar 

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Authors and Affiliations

  1. Doctor of Mathematics, Faculty of Mathematics, University of Łódź, Łódź, Poland

    T. Antczak

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  1. T. Antczak
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Antczak, T. Modified Ratio Objective Approach in Mathematical Programming. J Optim Theory Appl 126, 23–40 (2005). https://doi.org/10.1007/s10957-005-2654-5

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