Geodesic
A Partial Condition Number Theorem in Mathematical Programming
Journal of convex analysis, Tome 27 (2020) no. 2, pp. 777-79
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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.
Classification : 90C30, 90C31
Mots-clés : Condition number, condition number theorem, mathematical programming with data perturbations 
@article{JCA_2020_27_2_JCA_2020_27_2_a17,
     author = {T. Zolezzi},
     title = {A {Partial} {Condition} {Number} {Theorem} in {Mathematical} {Programming}},
     journal = {Journal of convex analysis},
     pages = {777--79},
     year = {2020},
     volume = {27},
     number = {2},
     url = {http://geodesic.mathdoc.fr/item/JCA_2020_27_2_JCA_2020_27_2_a17/}
}
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T. Zolezzi. A Partial Condition Number Theorem in Mathematical Programming. Journal of convex analysis, Tome 27 (2020) no. 2, pp. 777-79. http://geodesic.mathdoc.fr/item/JCA_2020_27_2_JCA_2020_27_2_a17/