I know that summation of two convex functions is also convex but I would like to know that does the same holds true for non-convex functions also such that the summation of two non-convex functions also non-convex?
2026-03-28 13:30:50.1774704650
Convexity analysis
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No. Sum of two non-convex functions can be a convex function. Consider the following: $$\ f(x)=x^4-2x^3 \ , \ \ g(x)=2x^3 $$ We see that $h(x) = f(x)+g(x)=x^4$ is a convex function.