The effect of calmness on the solution set of systems of nonlinear equations
The authors address the problem of solving a system of continuously differentiable nonlinear equations under the condition of calmness (also called upper Lipschitz-continuity). The notion of calmness is quite useful in the study of the convergence properties of iterative methods and also has implications in connection with Karush-Kuhn-Tucker (KKT) systems. In this paper, the authors prove that the local error bound described by calmness, together with the continuous differentiability, imply that the rank of the Jacobian is locally constant on the solution set. They also prove that locally, the solution set must be a differentiable manifold.
scientific article; zbMATH DE number 6145967