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Robust duality for fractional programming problems with constraint-wise data uncertainty. (English) Zbl 1242.90252
This paper deals with duality theory for examining and solving convex-concave fractional programming in the face of data uncertainty. The authors prove strong duality between the robust counterpart of an uncertain convex-concave fractional program and the optimistic counterpart of its conventional Wolfe dual program with uncertain parameters. For linear fractional programming problems with constraint-wise interval uncertainty, it is shown that the dual of the robust counterpart is indeed equivalent to the optimistic counterpart. Consequently, the authors also establish that a robust (worst-case) solution of a linear fractional programming problem with constraint-wise interval uncertainty can be found by solving a simple linear programming problem. It would be of interest to investigate whether strong duality can be used to find robust solutions of linear fractional problems easily with broad classes of uncertainty sets including the ellipsoidal uncertainty set that is often employed in robust optimization.

MSC:
90C32 Fractional programming
90C46 Optimality conditions and duality in mathematical programming
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