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An implicit function theorem
Authors:K Jittorntrum
Institution:(1) Computing Research Group, Australian National University, Canberra, Australia
Abstract:Suppose thatF:DsubR n×RmrarrRn, withF(x 0,y 0)=0. The classical implicit function theorem requires thatF is differentiable with respect tox and moreover that part1 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.
Keywords:Implicit function theorem  nonlinear programming
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