Journal of Convex Analysis 19 (2012), No. 4, 913--926
Copyright Heldermann Verlag 2012
Regularity Modulus of Intersection Mappings. Application to the Stability of Equations via Splitting into Inequalities
María Josefa Cánovas
Center of Operations Research, Miguel Hernández University, 03202 Elche - Alicante, Spain
canovas@umh.es
Francisco José Gómez-Senent
Center of Operations Research, Miguel Hernández University, 03202 Elche - Alicante, Spain
paco.gomez@umh.es
Juan Parra
Center of Operations Research, Miguel Hernández University, 03202 Elche - Alicante, Spain
parra@umh.es
This paper is firstly concerned with the modulus of metric regularity of intersection mappings. We consider a finite collection of set-valued mappings and analyze the relationship between the regularity moduli of these mappings (specifically, the maximum of them) and the regularity modulus of the associated intersection mapping. As an application we derive the Lipschitz modulus of the feasible set mapping associated with linear systems of (possibly) infinitely many linear inequalities and finitely many equations. Previously we characterize the metric regularity of such systems. Specifically, we consider an intersection mapping which obeys the strategy of splitting equations into inequalities, and then we apply preliminary results for inequality systems.
Keywords: Metric regularity, linear systems, intersection mappings, linear regularity.
MSC: 65F22, 90C34, 90C05, 15A39, 49J53
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