Questions on the optimization functions of Mathematica such as FindMinimum/FindMaximum, Minimize/Maximize, NMinimize/NMaximize, etc.

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How to describe the convex hull of a set of points as an implicit region for optimization?

In Mathematica you can create out of a set of points in 2D and 3D the convex hull and use it as a region for optimization problem, e.g., ...