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I want to understand why do we have to define a function on convex set before we define concavity or convexity.

https://mjo.osborne.economics.utoronto.ca/index.php/tutorial/index/1/CVN/t#d:CvxSet

I am reading this and I dont understand why they explained convex sets before explaining concavity and convexity.

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  • $\begingroup$ That makes sense, thank you! $\endgroup$
    – Damien
    Sep 30, 2021 at 4:26
  • $\begingroup$ @markleeds Please post answers as answers. $\endgroup$
    – Giskard
    Sep 30, 2021 at 6:12

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Hi: The connection between convex sets and convex ( and concave ) functions is that convex ( and concave ) functions should be defined on convex sets because, if the sets are defined on sets that are not convex, then there may be points on the set where the convex (and concave ) function is not defined.

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