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

Amos Uderzo

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arXiv · 1703.10552

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

Amos Uderzo

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Abstract

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

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Amos Uderzo. 2017-04-05. An implicit multifunction theorem for the hemiregularity of mappings with application to constrained optimization. https://arxiv.org/abs/1703.10552

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