On robust duality for fractional programming with uncertainty data

On robust duality for fractional programming with uncertainty data In this paper, we present a duality theory for fractional programming problems in the face of data uncertainty via robust optimization. By employing conjugate analysis, we establish robust strong duality for an uncertain fractional programming problem and its uncertain Wolfe dual programming problem by showing strong duality between the deterministic counterparts: robust counterpart of the primal model and the optimistic counterpart of its dual problem. We show that our results encompass as special cases some programming problems considered in the recent literature. Moreover, we also show that robust strong duality always holds for linear fractional programming problems under scenario data uncertainty or constraint-wise interval uncertainty, and that the optimistic counterpart of the dual is tractable computationally. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Positivity Springer Journals

On robust duality for fractional programming with uncertainty data

Positivity , Volume 18 (1) – Feb 12, 2013
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Publisher
Springer Basel
Copyright
Copyright © 2013 by Springer Basel
Subject
Mathematics; Fourier Analysis; Operator Theory; Potential Theory; Calculus of Variations and Optimal Control; Optimization; Econometrics
ISSN
1385-1292
eISSN
1572-9281
D.O.I.
10.1007/s11117-013-0227-7
Publisher site
See Article on Publisher Site

Abstract

In this paper, we present a duality theory for fractional programming problems in the face of data uncertainty via robust optimization. By employing conjugate analysis, we establish robust strong duality for an uncertain fractional programming problem and its uncertain Wolfe dual programming problem by showing strong duality between the deterministic counterparts: robust counterpart of the primal model and the optimistic counterpart of its dual problem. We show that our results encompass as special cases some programming problems considered in the recent literature. Moreover, we also show that robust strong duality always holds for linear fractional programming problems under scenario data uncertainty or constraint-wise interval uncertainty, and that the optimistic counterpart of the dual is tractable computationally.

Journal

PositivitySpringer Journals

Published: Feb 12, 2013

References

  • Li, G.Y: Lagrange multiplier characterizations of robust best approximations under constraint data uncertainty
    Jeyakumar, V; Wang, JH

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