If you know the standard English meaning of the words convex and concave, you can remember that for a convex function it is the epigraph that is convex, and for a concave function it is the epigraph that is …

Mar 27, 2015 · It is (strictly) concave. However, some books or lecture notes use "convex" for both convex and concave, adding an adjective "upward" or "downward" -- which can be confusing.

Then, if the determinant of the Hessian matrix is greater than $0$, then the function is strictly convex. If the determinant of the Hessian is equal to $0$, then the Hessian is positive semi-definite and the …

Sep 29, 2018 · I want to analyze two Hessian matrices regarding definiteness to formulate conclusions whether the functions are convex or concave. If you could check my thoughts, I’d be grateful.

Nov 1, 2017 · What's the intuitive difference between quasi-concavity and concavity? Can you give an example of a quasi-concave function that is not concave?

Concave (inward-curved) lenses are the opposite of convex lenses, so there is a pre-existing word for "not convex" or "convex in the opposite direction". Convex has an absolutely entrenched …

@Lost1, there are actually four such rules, for each combination of convex/concave inner and outer functions: convex-nondecreasing & convex -> convex, convex-nonincreasing & concave -> convex, …

Sep 5, 2015 · quasi convex quasi concave, and semi-strict quasi concave and semi-strict quasi convex, and strictly quasi concave and strictly quasi concave. In addition it will be strictly pseudo convex. as …

3 Because you didn't specify the domain and range, assume f is a real function. Also, so the inverse is defined, assume f is one-to-one. Thus f is either increasing or decreasing. Now the inverse of f …

Jun 28, 2020 · The definition of a convex function,is: "An interval is called convex if the line segment between any two points on the graph of the function lies above or on the graph." …