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Characterizations of error bounds for lower semicontinuous functions on metric spaces. (English) Zbl 1085.49019

In the first part of the paper the authors provide characterizations of the existence of global and local error bounds for lower semicontinuous functions on complete metric spaces using the strong slope. Then they consider the convex case in which one relates the strong slope with other known expressions for the Hoffman constant. In the last section of the paper one studies the local metric regularity for closed multi-functions between complete metric spaces.

MSC:

49J52 Nonsmooth analysis
90C46 Optimality conditions and duality in mathematical programming
49J53 Set-valued and variational analysis
90C25 Convex programming
90C26 Nonconvex programming, global optimization
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