Generalized Fractional Programming With User Interaction
AbstractThe present paper proposes a new approach to solve generalized fractional programming problems through user interaction. Capitalizing on two alternatives, we review the Dinkelbach-type methods and set forth the main difficulty in applying these methods. In order to cope with this difficulty, we propose an approximation approach that can be controlled by a predetermined parameter. The proposed approach is promising particularly when a decision maker is involved in the solution process and agrees upon finding an effective but nearoptimal value in an efficient manner. The decision maker is asked to decide the parameter and our analysis shows how good is the value found by the approximation corresponding to this parameter. In addition, we present several observations that may be suitable for boosting up the performance of the proposed approach. Finally, we support our discussion through extensive numerical experiments.
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Bibliographic InfoPaper provided by Erasmus Research Institute of Management (ERIM), ERIM is the joint research institute of the Rotterdam School of Management, Erasmus University and the Erasmus School of Economics (ESE) at Erasmus University Rotterdam. in its series Research Paper with number ERS-2004-033-LIS.
Date of creation: 21 Jun 2004
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Web page: http://www.erim.eur.nl/
approximation approach; error analysis; generalized fractional programming; performance improvement; user interaction;
This paper has been announced in the following NEP Reports:
- NEP-ALL-2005-02-20 (All new papers)
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- R. Jagannathan, 1985. "An Algorithm for a Class of Nonconvex Programming Problems with Nonlinear Fractional Objectives," Management Science, INFORMS, vol. 31(7), pages 847-851, July.
- Frenk, J.B.G. & Schaible, S., 2004. "Fractional Programming," Research Paper ERS-2004-074-LIS, Erasmus Research Institute of Management (ERIM), ERIM is the joint research institute of the Rotterdam School of Management, Erasmus University and the Erasmus School of Economics (ESE) at Erasmus Uni.
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