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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 have left out the y-axis in the sketch, but it is obvious where it should be... – Brooke Knight Jul 27 '11 at 15:15
up vote 3 down vote accepted

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! – Brooke Knight Jul 27 '11 at 15:31

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