Journal of Optimization Theory and Applications

, Volume 25, Issue 4, pp 575–577

An implicit function theorem

  • K. Jittorntrum
Technical Note


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 theorem nonlinear programming 


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Copyright information

© Plenum Publishing Corporation 1978

Authors and Affiliations

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

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