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Journal of Convex Analysis 27 (2020), No. 2, 777--790
Copyright Heldermann Verlag 2020

A Partial Condition Number Theorem in Mathematical Programming

Tullio Zolezzi
Dip. di Matematica, UniversitÓ di Genova, 16146 Genova, Italy

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 well-conditioning is obtained. It is shown that the distance to ill-conditioning 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.

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