La programmation mathématique multicritère et la gestion des ressources en eau
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...
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...
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...
In this paper, we study local stability of the mean-risk model with Conditional Value at Risk measure where the mixed-integer value function appears as a loss variable. This model has been recently introduced and studied in~Schulz and Tiedemann [16]. First, we generalize the qualitative results for the case with random technology matrix. We employ the contamination techniques to quantify a possible effect of changes in the underlying probability distribution on the optimal value. We use the generalized...