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Journal of Convex Analysis 30 (2023), No. 3, 1001--1023
Copyright Heldermann Verlag 2023

On the Isolated Calmness Property of Implicitly Defined Multifunctions

Helmut Gfrerer
Institute of Computational Mathematics, Johannes Kepler University, Linz, Austria

Jirí V. Outrata
(1) Inst. Information Theory and Automation, Czech Acad. of Sciences, Prague, Czech Republic
(2) Centre for Informatics and Appl. Optimization, Federation University, Ballarat, Australia

The paper deals with an extension of the available theory of SCD (subspace containing derivatives) mappings to mappings between spaces of different dimensions. This extension enables us to derive workable sufficient conditions for the isolated calmness of implicitly defined multifunctions around given reference points. This stability property differs substantially from isolated calmness at a point and, possibly in conjunction with the Aubin property, offers a new useful stability concept. The application area includes a broad class of parameterized generalized equations, where the respective conditions ensure a rather strong type of Lipschitzian behavior of their solution maps.

Keywords: Strong metric subregularity and isolated calmness on a neighborhood, generalized derivatives, semismoothness*, implicit multifunctions.

MSC: 65K10, 65K15, 90C33.

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