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The present paper contains some investigations about a uniform variant of thenotion of metric hemiregularity, the latter being a less explored propertyobtained by weakening metric regularity. The introduction of such aquantitative stability property for set-valued mappings is motivated byapplications to the penalization of constrained optimization problems, throughthe notion of problem calmness. As a main result, an implicit multifunctiontheorem for parameterized inclusion problems is established, which measures theuniform hemiregularity of the related solution mapping in terms of problemdata. A consequence on the exactness of penalty functions is discussed.

An implicit multifunction theorem for the hemiregularity of mappings with application to constrained optimization