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Nonlinear objectives, nonlinear constraints, non-convex objective, non-convex feasible region.

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Number of local minima of a particular non-convex composite function

I am interested in proving that the following equation on the interval $x \in [c,1]$ is minimized either at the endpoints or where $x=\sqrt{c}$: $f(x)=\frac{-1}{\log(1-x)}+\frac{-1}{\log(1-\frac{c}{x …