Local and Global Inverse and Implicit Function Theorems

Abstract: In the talk, we present a local inverse function theorem on a cone in a neighbourhood of abnormal point. We present a global inverse function theorem in the form of theorem on trivial bundle, guaranteeing that if a smooth mapping of finite-dimensional spaces is uniformly nonsingular, then it has a smooth right inverse satisfying a priori estimate. We also present a global implicit function theorem guaranteeing the existence and continuity of a global implicit function under the condition that the mappings in question are uniformly nonsingular. The generalization of these results to the case of mappings of Hilbert spaces and Banach spaces are discussed.

optimization and control

Audience: researchers in the topic

Variational Analysis and Optimisation Webinar

Series comments: Register on www.mocao.org/va-webinar/ to receive information about the zoom connection.