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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  1. 1.
    Ortega, J. M., andRheinboldt, W. C.,Iterative Solution of Nonlinear Equations in Several Variables, Academic Press, New York, New York, 1970.Google Scholar
  2. 2.
    Greenberg, M.,Lectures on Algebraic Topology, W. A. Benjamin, Menlo Park, California, 1971.Google Scholar

Copyright information

© Plenum Publishing Corporation 1978

Authors and Affiliations

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

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