The Proof And Applications Of The Generalized Implicit Function Theorem In Optimization

This thesis mainly concerned with generalized implicit function theorem andits application, we proved the generalized implicit function theorem instead of theClarke generalized gradient, This paper is motivated by Kummer and Klatte withregard to non-smooth equations in optimization.It uses more basic methods andproofs the generalized implicit function theorem easily again. In this paper,theproof of the generalized implicit function theorem uses apagoge that we all know.At the last of this paper, we extend the Lipschitz continuous result of KKTsystem witch Shvartsman has proved with implicit function theorem, we mainlychange the condition that independent to CRCQ, what’s more, we use CRCQ andsome lemmas proving the exist of the solution mapping and its Lipschitz continuityunder some weaker conditions.