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A sufficient condition for global invertibility of Lipschitz mapping

S. Tarasov

TL;DR

It is shown that S.Vavasis' sufficient condition for global invertibility of a polynomial mapping can be easily generalized to the case of a general Lipschitz mapping.

Abstract

We show that S.Vavasis' sufficient condition for global invertibility of a polynomial mapping can be easily generalized to the case of a general Lipschitz mapping. Keywords: Invertibility conditions, generalized Jacobian, nonsmooth analysis.

A sufficient condition for global invertibility of Lipschitz mapping

TL;DR

It is shown that S.Vavasis' sufficient condition for global invertibility of a polynomial mapping can be easily generalized to the case of a general Lipschitz mapping.

Abstract

We show that S.Vavasis' sufficient condition for global invertibility of a polynomial mapping can be easily generalized to the case of a general Lipschitz mapping. Keywords: Invertibility conditions, generalized Jacobian, nonsmooth analysis.

Paper Structure

This paper contains 1 theorem, 1 equation.

Key Result

Theorem 1

Let $F(\cdot)=(f^1(\cdot),\dots,f^n(\cdot)): U \subseteq {\bf R}^n \rightarrow {\bf R}^n$ be any Lipschitz mapping defined on the convex reference domain $U$. If the set of the generalized Jacobians ${\cal J}=\{J \in \partial F(u),\, u \in U\}$ forms a strict $V$-family then $F(\cdot)$ is globally i

Theorems & Definitions (1)

  • Theorem 1