An implicit function theorem |
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Authors: | K Jittorntrum |
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Institution: | (1) Computing Research Group, Australian National University, Canberra, Australia |
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Abstract: | Suppose thatF:DR
n×RmRn, 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. |
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Keywords: | Implicit function theorem nonlinear programming |
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