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On Rohn’s relative sensitivity coefficient of the optimal value for a linear-fractional program. (English) Zbl 1030.90125

Summary: In this note we consider a linear-fractional programming problem with equality linear constraints. Following Rohn, we define a generalized relative sensitivity coefficient measuring the sensitivity of the optimal value for a linear program and a linear-fractional minimization problem with respect to the perturbations in the problem data.

By using an extension of Rohn’s result for the linear programming case, we obtain, via Charnes-Cooper variable change, the relative sensitivity coefficient for the linear-fractional problem. This coefficient involves only the measure of data perturbation, the optimal solution for the initial linear-fractional problem and the optimal solution of the dual problem of linear programming equivalent to the initial fractional problem.

MSC:
90C31Sensitivity, stability, parametric optimization
90C32Fractional programming