Robust Duality for Fractional Programming Problems with Constraint‐Wise Data Uncertainty

Robust Duality for Fractional Programming Problems with Constraint‐Wise Data Uncertainty

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Article ID: iaor201110518
Volume: 151
Issue: 2
Start Page Number: 292
End Page Number: 303
Publication Date: Nov 2011
Journal: Journal of Optimization Theory and Applications
Authors: ,
Keywords: stochastic processes, programming: linear
Abstract:

In this paper, we examine duality for fractional programming problems in the face of data uncertainty within the framework of robust optimization. We establish 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, we show that the dual of the robust counterpart is the optimistic counterpart in the sense that they are equivalent. Our results show that a worst‐case solution of an uncertain fractional program (i.e., a solution of its robust counterpart) can be obtained by solving a single deterministic dual program. In the case of a linear fractional programming problem with interval uncertainty, such solutions can be found by solving a simple linear program.

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