Journal of Optimization Theory and Applications

, Volume 25, Issue 4, pp 575–577

An implicit function theorem

  • K. Jittorntrum
Technical Note

DOI: 10.1007/BF00933522

Cite this article as:
Jittorntrum, K. J Optim Theory Appl (1978) 25: 575. doi:10.1007/BF00933522

Abstract

Suppose thatF:D⊂Rn×Rm→Rn, withF(x0,y0)=0. The classical implicit function theorem requires thatF is differentiable with respect tox and moreover that ∂1F(x0,y0) is nonsingular. We strengthen this theorem by removing the nonsingularity and differentiability requirements and by replacing them with a one-to-one condition onF as a function ofx.

Key Words

Implicit function theoremnonlinear programming

Copyright information

© Plenum Publishing Corporation 1978

Authors and Affiliations

  • K. Jittorntrum
    • 1
  1. 1.Computing Research GroupAustralian National UniversityCanberraAustralia