
Journal of Convex Analysis 27 (2020), No. 2, 777790 Copyright Heldermann Verlag 2020 A Partial Condition Number Theorem in Mathematical Programming Tullio Zolezzi Dip. di Matematica, Università di Genova, 16146 Genova, Italy zolezzi@dima.unige.it A condition number of mathematical programming problems is defined as a measure of the sensitivity of their global optimal solutions under general perturbations described by parameters acting on their data. A (pseudo) distance among problems fulfilling prescribed bounds is defined via the corresponding augmented Kojima functions. A characterisation of wellconditioning is obtained. It is shown that the distance to illconditioning is bounded from above by a multiple of the reciprocal of the condition number. This upper bound extends to general perturbed problems known results dealing with canonical perturbations. Keywords: Condition number, condition number theorem, mathematical programming with data perturbations. MSC: 90C30, 90C31. [ Fulltextpdf (112 KB)] for subscribers only. 