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.
Finding an equation to a function
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functions
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0Oops, I h$a$ve left out the y-axis in the sketch, but it is obvious where it should be... – 2011-07-27
1 Answers
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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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0Of course, silly me. Thanks! – 2011-07-27