Resumen de Stability of a parametric family of linear inequality systems when the strong slater condition fails

María Josefa Cánovas Cánovas, Marco A. López Cerdá, Juan Parra López

• If we consider the parameter space of all linear inequality systems with a fixed and arbitrary index set, with the topology of the uniform convergence of the coefficient vectors, then the Strong Slater condition (SSC) is equivalent to the lower semicontinuity (lsc) of the feasible set mapping, F. When we change this scenario by a parametric setting, both properties turn out to be independent. Under the equicontinuity of the coefficient functions, the SSC is shown to be sufficient for the lsc of F. When the SSC fails, we characterize the lsc of F in terms of the family of characteristic cones and their behaviour w.r.t. the trivial inequality 0 ³ 0.