
Journal of Convex Analysis 23 (2016), No. 4, 12471262 Copyright Heldermann Verlag 2016 A Condition Number Theorem in Convex Programming without Uniqueness Tullio Zolezzi Dipartimento di Matematica, Università di Genova, via Dodecaneso 35, 16146 Genova, Italy zolezzi@dima.unige.it A condition number of mathematical programming problems with convex data is defined as a suitable measure of the sensitivity of their optimal solutions under canonical perturbations. A pseudodistance among mathematical programming problems is introduced via the corresponding Kojima functions. Characterizations of wellconditioning are obtained. We prove that the distance to illconditioning is bounded from above by a multiple of the reciprocal of the condition number, thereby generalizing previous results dealing with problems with a unique optimal solution. Keywords: Convex programming, condition number, distance to illconditioning, condition number theorem. MSC: 90C31, 90C25 [ Fulltextpdf (141 KB)] for subscribers only. 