calmness generalized equations Lipschitz functions first order methods crucial linear systems modified mappings Characterization of Calmness for Banach space mappings Jan Heerda Heerda Jan Bernd Kummer Kummer Bernd Institut für Mathematik, Humboldt-Universität zu Berlin (ISSN 0863-0976),

Characterization of Calmness for Banach space mappings

Jan Heerda , Bernd Kummer

Preprint series: Institut für Mathematik, Humboldt-Universität zu Berlin (ISSN 0863-0976),

MSC 2000

49J52 Nonsmooth analysis
49K40 Sensitivity, stability, well-posedness

Abstract
We characterize calmness of multifunctions explicitly by calmness of level sets to globally Lipschitz functions, by convergence of specific solution methods for the related inclusions as well as by solvability of crucial linear systems. As a main tool, a so-called relative slack function will be applied. In this way, also equivalence between calmness and metric regularity of specific subsystems will be derived.

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