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I can think of a visual example s.t. f in $\mathbf C^2$ ($\mathbf R^2$) has a single local minimum stationary point that is not a global minimum but I can't give it a concrete equation... If anyone can think of a better example (i.e. one with a simpler equation) that would be even better! Thanks. My example

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    Oops, I h$a$ve left out the y-axis in the sketch, but it is obvious where it should be...2011-07-27

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How about just subtracting a Gaussian from an exponential, e.g.

$f(x) = e^y - \frac 3 4 e^{-x^2-y^2}$

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    Of course, silly me. Thanks!2011-07-27