On the isolated calmness property of implicitly defined multifunctions

TL;DR

This paper extends the theory of SCD mappings to different-dimensional spaces, providing new conditions for the isolated calmness of implicitly defined multifunctions, which enhances understanding of their stability and Lipschitz behavior.

Contribution

It introduces a novel extension of SCD mapping theory to diverse-dimensional spaces, enabling the derivation of sufficient conditions for isolated calmness of implicit multifunctions.

Findings

Derived workable sufficient conditions for isolated calmness.

Extended SCD theory to mappings between different-dimensional spaces.

Ensured strong Lipschitzian behavior of solution maps in generalized equations.

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 Lipschitztan behavior of their solution maps.