F. J. Toledo Melero, M. J. Cánovas Cánovas, M. A. López-Cerdá, J. Parra López
The calmness modulus of the optimal solution set (argmin) mapping of a parameterized linear program provides a local deformation rate of this solution set with respect to the parameter perturbation size. In this talk we provide an overview on this calmness modulus in two perturbations settings: the one of canonical perturbations (perturbations of the objective function as well as the right-hand-side of the constraints), and the framework of full perturbations (where the left-hand-side coefficients may be also perturbed). We provide a pointbased expression (depending only on the nominal data) for the calmness modulus of the argmin mapping under canonical perturbations, which leads to an upper bound in the case of full perturbations. We specially focus on the role played by the size of the objective function coefficient vector in relation to this upper bound, which turns out to be attained if and only if this size is below a critical threshold. An illustrative example is carried out.
Palabras clave: Linear programming, calmness, argmin mappingProgramado
L08.4 Optimización Lineal, Estocástica y Robusta
5 de septiembre de 2016 15:40