Stability of Error Bounds for Semi-infinite Convex Constraint Systems | Zendy

Huynh Van Ngai | Zendy; Alexander Y. Kruger | Zendy; Michel Théra | Zendy

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Stability of Error Bounds for Semi-infinite Convex Constraint Systems

Author(s) -

Huynh Van Ngai,

Alexander Y. Kruger,

Michel Théra

Publication year - 2010

Publication title -

siam journal on optimization

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 2.066

H-Index - 136

eISSN - 1095-7189

pISSN - 1052-6234

DOI - 10.1137/090767819

Subject(s) - mathematics , subderivative , constraint (computer aided design) , stability (learning theory) , regular polygon , upper and lower bounds , convex optimization , convex combination , convex set , sensitivity (control systems) , mathematical analysis , geometry , computer science , electronic engineering , engineering , machine learning

In this paper, we are concerned with the stability of the error bounds for semi-infinite convex constraint systems. Roughly speaking, the error bound of a system of inequalities is said to be stable if all its “small” perturbations admit a (local or global) error bound. We first establish subdifferential characterizations of the stability of error bounds for semi-infinite systems of convex inequalities. By applying these characterizations, we extend some results established by Azé and Corvellec [SIAM J. Optim., 12 (2002), pp. 913-927] on the sensitivity analysis of Hoffman constants to semi-infinite linear constraint systems.

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