Should the function be a] Piecewise affine or b] Convex and piecewise affine?
I'm doing the MOOC on Convex Optimization by Stephen Boyd and came across this question in the exercises. The answer which is given there is b] but I think a] suffices.
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How do you define polyhedron? – gerw Sep 15 '16 at 18:04
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@gerw a polyhedron is the solution set of a finite number of linear equalities and inequalities – niranjantdesai Sep 20 '16 at 09:47
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Hint: According to your definition, a polyhedron is always convex. What about the epigraph of a function?
gerw
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the epigraph of a function is convex set if and only if the function is convex. Oh, got it! Because the polyhedron (which is the epigraph in this case) is convex, the function has to be convex. – niranjantdesai Sep 23 '16 at 13:06