VA & Opt Webinar: Aram Arutyunov & S.E. Zhukovskiy

Title: Local and Global Inverse and Implicit Function Theorems

Speaker: Aram Arutyunov (Moscow State University) & S.E. Zhukovskiy (V. A. Trapeznikov Institute of Control Sciences of RAS)

Date and Time: November 18th, 2020, 17:00 AEDT (Register here for remote connection via Zoom)

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.