Let S CR be a nonempty convex set. Let h: SR be a convex function, and...

 

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Let S CR be a nonempty convex set. Let h: SR be a convex function, and let g: R R be a monotonically non-decreasing convex function over the set {h(x): x = S}. Show that the composition function is convex. f(x) = g(h(x)) Let S CR be a nonempty convex set. Let h: SR be a convex function, and let g: R R be a monotonically non-decreasing convex function over the set {h(x): x = S}. Show that the composition function is convex. f(x) = g(h(x))