Cánovas Cánovas, María Josefa, López Cerdá, Marco A., Parra López, Juan, Toledo, Francisco Javier
Distance to Ill-Posedness in Linear Optimization via the Fenchel-Legendre Conjugate
Journal of Optimization Theory and Applications. 2006, 130(2): 173-183. doi:10.1007/s10957-006-9097-5
URI: http://hdl.handle.net/10045/75170
DOI: 10.1007/s10957-006-9097-5
ISSN: 0022-3239 (Print)
Abstract: 
We consider the parameter space of all the linear inequality systems, in the n-dimensional Euclidean space and with a fixed index set, endowed with the topology of the uniform convergence of the coefficient vectors. A system is ill-posed with respect to the consistency when arbitrarily small perturbations yield both consistent and inconsistent systems. In this paper, we establish a formula for measuring the distance from the nominal system to the set of ill-posed systems. To this aim, we use the Fenchel-Legendre conjugation theory and prove a refinement of the formula in Ref. 1 for the distance from any point to the boundary of a convex set.
Keywords:Fenchel-Legendre conjugate, Stability, Well-posedness, Linear inequality systems, Distance to ill-posedness
Kluwer Academic Publishers-Plenum Publishers
info:eu-repo/semantics/article