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Linear fractional program under interval and ellipsoidal uncertainty

Maziar Salahi, Saeed Fallahi (2013)

Kybernetika

In this paper, the robust counterpart of the linear fractional programming problem under linear inequality constraints with the interval and ellipsoidal uncertainty sets is studied. It is shown that the robust counterpart under interval uncertainty is equivalent to a larger linear fractional program, however under ellipsoidal uncertainty it is equivalent to a linear fractional program with both linear and second order cone constraints. In addition, for each case we have studied the dual problems...

Lipschitz modulus in convex semi-infinite optimization via d.c. functions

María J. Cánovas, Abderrahim Hantoute, Marco A. López, Juan Parra (2009)

ESAIM: Control, Optimisation and Calculus of Variations

We are concerned with the Lipschitz modulus of the optimal set mapping associated with canonically perturbed convex semi-infinite optimization problems. Specifically, the paper provides a lower and an upper bound for this modulus, both of them given exclusively in terms of the problem’s data. Moreover, the upper bound is shown to be the exact modulus when the number of constraints is finite. In the particular case of linear problems the upper bound (or exact modulus) adopts a notably simplified...

Lipschitz modulus in convex semi-infinite optimization via d.c. functions

María J. Cánovas, Abderrahim Hantoute, Marco A. López, Juan Parra (2008)

ESAIM: Control, Optimisation and Calculus of Variations

We are concerned with the Lipschitz modulus of the optimal set mapping associated with canonically perturbed convex semi-infinite optimization problems. Specifically, the paper provides a lower and an upper bound for this modulus, both of them given exclusively in terms of the problem's data. Moreover, the upper bound is shown to be the exact modulus when the number of constraints is finite. In the particular case of linear problems the upper bound (or exact modulus) adopts a notably simplified...

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