Wednesday, 15:15 - 15:40 h, Room: H 2035

 

Alfredo Iusem
Th effect of calmness on the solution set of nonlinear equaltions

Coauthor: Roger Behling

 

Abstract:
We address the problem of solving a continuously differentiable nonlinear system of equations under the condition of calmness. This property, called also upper Lipschitz continuity in the literature, can be described as a local error bound, and is being widely used as a regularity condition in optimization. Indeed, it is known to be significantly weaker than classic regularity assumptions, which imply that solutions are isolated. We prove that under this condition, the rank of the Jacobian of the function that defines the system of equations must be locally constant on the solution set. As a consequence, we conclude that, locally, the solution set must be a differentiable manifold. Our results are illustrated by examples and discussed in terms of their theoretical relevance and algorithmic implications.

 

Talk 1 of the invited session Wed.3.H 2035
"Nonsmooth analysis with applications in engineering" [...]
Cluster 24
"Variational analysis" [...]

 

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