Stability of inclusions: characterizations via suitable Lipschitz functions and algorithms

This article deals with basic notions of local stability of solutions to generalized equations. The Aubin property, calmness, strong Lipschitz stability and other (Lipschitz) stability concepts are characterized by two classical approaches: by monotonicity of assigned Lipschitz functions and directly via the main applications of stability statements – the behavior of solutions methods. In this way, ‘stability’ will be characterized by several new conditions. We also show how known concepts, which are mainly based on characterizations via generalized derivatives and are widely distributed in the literature, can be derived in an essentially self-contained and straightforward manner. §Dedicated to Professor Diethard Pallaschke on the occasion of his 65th birthday.

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