Technical Note

Journal of Optimization Theory and Applications

, Volume 25, Issue 4, pp 575-577

First online:

An implicit function theorem

  • K. JittorntrumAffiliated withComputing Research Group, Australian National University

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Suppose thatF:D⊂R n×Rm→Rn, withF(x 0,y 0)=0. The classical implicit function theorem requires thatF is differentiable with respect tox and moreover that ∂1 F(x 0,y 0) 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