Abstract

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.

Author information

Contact details are reproduced from the original publication and may be historical.

Helmut Gfrerer

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

helmut.gfrerer@jku.at

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

outrata@utia.cas.cz

Keywords

  • Strong metric subregularity and isolated calmness on a neighborhood
  • generalized derivatives
  • semismoothness*
  • implicit multifunctions

Mathematics Subject Classification

65K10, 65K15, 90C33

Suggested citation

H. Gfrerer, J. V. Outrata. “On the Isolated Calmness Property of Implicitly Defined Multifunctions.” Journal of Convex Analysis 30 (2023), No. 3, 1001–1023.

Copyright Heldermann Verlag 2023