What is definition of a convex monotonic increasing function?

04 April 2017 1 343 Report

Hi, what is definition of a convex monotone increasing (or decreasing) function?is it possible that a convex function with a global minimum, be a monotonic increasing function? thanks

Stan Sykora

No, the presence of a any minimum, be it local or global, contradicts the requirement of monotonicity. One can of course usually find restricted domains in which such functions are monotonous. For example, y=x^2 is not monotonous in R but it is monotonously increasing in R+. Monotonicity is there not a property of a function, it is a property of the pair {function, domain}.

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