Journal of Convex Analysis 23 (2016), No. 4, 1247--1262
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 pseudo-distance among mathematical programming problems is introduced via the corresponding Kojima functions. Characterizations of well-conditioning are obtained. We prove that the distance to ill-conditioning 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 ill-conditioning, condition number theorem.
MSC: 90C31, 90C25
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