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Home > Articles > Published articles > Perturbation analysis of a condition number for convex inequality systems and global error bounds for analytic systems 
Date:  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 wellconditioned under these types of perturbations, where the wellconditionedness 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 wellconditionedness 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. . 
Language:  Anglès. 
Document:  Article ; recerca ; article ; publishedVersion 
Subject:  Condition numbers ; Analytic systems ; Convex inequality systems ; Levelcoercivity ; Recession functions ; Recession cones ; Perturbation analysis 
Published in:  Mathematical Programming, vol. 83 n. 2 (1998) p. 263276, ISSN 00255610 
14 p, 612.0 KB UAB restricted access 
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