celseylynn2475 celseylynn2475

15-04-2024
Mathematics

contestada

Given a function f : Rⁿ → R, its epigraph is defined as follows

epi f = {(x,t) ∈ Rⁿ⁺¹ : x ∈ Rⁿ, t ≥ f(x)}

Could someone please help me prove that a function is convex iff its epigraph is a convex set?

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