NDLI: Perturbation analysis of a condition number for convex inequality systems and global error bounds for analytic systems

Content Provider	Springer Nature Link
Author	Deng, Sien
Copyright Year	1998
Abstract	In this paper several types of perturbations on a convex inequality system are considered, and conditions are obtained for the system to be well-conditioned under these types of perturbations, where the well-conditionedness of a convex inequality system is defined in terms of the uniform boundedness of condition numbers under a set of perturbations. It is shown that certain types of perturbations can be used to characterize the well-conditionedness of a convex inequality system, in which either the system has a bounded solution set and satisfies the Slater condition or an associated convex inequality system, which defines the recession cone of the solution set for the system, satisfies the Slater condition. Finally, sufficient conditions are given for the existence of a global error bound for an analytic system. It is shown that such a global error bound always holds for any inequality system defined by finitely many convex analytic functions when the zero vector is in the relative interior of the domain of an associated convex conjugate function.
Starting Page	263
Ending Page	276
Page Count	14
File Format	PDF
ISSN	00255610
Journal	Mathematical Programming
Volume Number	83
Issue Number	1-3
e-ISSN	14364646
Language	English
Publisher	Springer-Verlag
Publisher Date	1998-01-01
Publisher Place	Berlin, Heidelberg
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Condition numbers Analytic systems Convex inequality systems Level-coercivity Recession functions Recession cones Perturbation analysis Calculus of Variations and Optimal Control; Optimization Mathematics of Computing Numerical Analysis Combinatorics Mathematical and Computational Physics Mathematical Methods in Physics
Content Type	Text
Resource Type	Article
Subject	Mathematics Software

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