Failure of the Only-Critical-Point-in-Town Test


Here is  a polynomial example of the failure of the only-critical-point-in-town test. There is a local minimum, it is the only critical point, but it is not an absolute minimum. This function, found by Calvert and Vamanamurthy, is simply z = x^2 (1 + y)^3 + 7 y^2.

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