María Jesús Gisbert Francés

University Carlos III de Madrid | UC3M · Department of Statistics

The present paper is devoted to the computation of the Lipschitz modulus of the optimal value function restricted to its domain in linear programming under different types of perturbations. In the first stage, we study separately perturbations of the right-hand side of the constraints and perturbations of the coefficients of the objective function....

In this paper, we use a geometrical approach to sharpen a lower bound given in [5] for the Lipschitz modulus of the optimal value of (finite) linear programs under tilt perturbations of the objective function. The key geometrical idea comes from orthogonally projecting general balls on linear subspaces. Our new lower bound provides a computable exp...

The paper is focussed on the Lipschitz lower semicontinuity of the feasible set mapping for linear (finite and infinite) inequality systems in three different perturbation frameworks: full, right-hand side and left-hand side perturbations. Inspired by [14], we introduce the Lipschitz lower semicontinuity-star as an intermediate notion between the L...

The final goal of the present paper is computing/estimating the calmness modulifrom below and above of the optimal value function restricted to the set of solvable linear problems.Roughly speaking, these moduli provide measures of the maximum rates of decrease and increaseof the optimal value under perturbations of the data (provided that solvabili...