Proof that the Epigraph of a Convex Function is a Convex Set
Students sometimes struggle to differentiate between the convexity of the function itself (where line segments between two points on the graph lie above or on the graph) and the convexity of the *set* , which includes all points *above* the graph, not just on it. The inclusion of the component is key.
Institutional Reference: Fundamentals of Optimization
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