Geodesic
A Condition Number Theorem in Convex Programming without Uniqueness
Journal of convex analysis, Tome 23 (2016) no. 4, pp. 1247-1262
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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.
Classification : 90C31, 90C25
Mots-clés : Convex programming, condition number, distance to ill-conditioning, condition number theorem 
@article{JCA_2016_23_4_JCA_2016_23_4_a11,
     author = {T. Zolezzi},
     title = {A {Condition} {Number} {Theorem} in {Convex} {Programming} without {Uniqueness}},
     journal = {Journal of convex analysis},
     pages = {1247--1262},
     year = {2016},
     volume = {23},
     number = {4},
     url = {http://geodesic.mathdoc.fr/item/JCA_2016_23_4_JCA_2016_23_4_a11/}
}
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T. Zolezzi. A Condition Number Theorem in Convex Programming without Uniqueness. Journal of convex analysis, Tome 23 (2016) no. 4, pp. 1247-1262. http://geodesic.mathdoc.fr/item/JCA_2016_23_4_JCA_2016_23_4_a11/