Resumen de Ameasure of stability and well-posedness of linear semi-infinite inequaltity systems

María Josefa Cánovas Cánovas , Marco A. López Cerdá , Juan Parra López , Francisco Javier Toledo Melero

• We consider the parameter space of all the linear inequality systems, in the n-dimensional Euclidean space, with a fixed and arbitrary index set, endowed with the topology of the uniform convergence of the coefficient vectors by means of an extended distance. Some authors consider that a system in the boundary of the set of all the consistent systems is ill-posed. Moreover, the distance to ill-posedness is closely related to the convergence of certain algorithms for solving the system. This paper provides two different expressions to calculate the distance to ill-posedness.