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, 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 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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