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I am looking for an example of a locally optimal point of the nonlinear program: $$\{ \min f(x) , g_i(x) \geq 0 \}$$ that does not have a singleton feasibility set.

e.g. not the example of $\{ \min x, x^2\leq 0 \} $ found here where the feasibility set is just $\{0\}$.

Sundar
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shnnnms
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    Example 4.5.3 and Solution 4.5.4 of https://www.math.uni-bielefeld.de/~drust/opt2017-part4.pdf provides such an example as per my comment at https://math.stackexchange.com/questions/4418465/what-is-the-meaning-of-local-optimality-in-nlp-mentioned-in-constraint-qualifi/4418601?noredirect=1#comment9246143_4418601 – Mark L. Stone Apr 03 '22 at 16:31

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