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Characterization of metric regularity for \({\sigma}\)-subsmooth multifunctions. (English) Zbl 1284.49019

Summary: In terms of the coderivative, we provide characterizations of metric subregularity for \({\sigma}\)-subsmooth multifunctions and extend some existing results on metric subregularity. We also establish Robinson-Ursescu type theorems for \({\sigma}\)-subsmooth multifunctions and approximately convex multifunctions. As applications, we study error bounds for nonconvex inequalities and Lipschitz property for multifunctions.

MSC:

49J53 Set-valued and variational analysis
49J52 Nonsmooth analysis
90C29 Multi-objective and goal programming
90C30 Nonlinear programming
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