Preliminaries of optimization theory Shapley–Folkman lemma

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the sine function non-convex.



epi(f) = { (x, u) : f(x) ≤ u }.


a real-valued function defined convex function if epigraph convex set.

for example, quadratic function f(x) = x convex, absolute value function g(x) = |x|. however, sine function (pictured) non-convex on interval (0, π).








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