Journal Home Page

Cumulative Index

List of all Volumes

Complete Contents
of this Volume

Previous Article

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, UniversitÓ di Genova, via Dodecaneso 35, 16146 Genova, Italy

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

[ Fulltext-pdf  (141  KB)] for subscribers only.