Jan 14, 2017 · A different definition is that a function is convex iff its epigraph is convex. This is a visually intuitive definition, and it explains why we use the same word "convex" for both sets …

May 14, 2018 · So, is there a way to distinguish convexity and strict convexity just by visual inspection of the graph of a function? And, if so, how? What can be the specific characteristic …

Apr 3, 2014 · Joint convexity means that the restriction of the function to any segment is a convex function of a single variable. Element-wise convexity means that only vertical and horizontal …

1 It is easy to prove if you write out (2) based on the definition of convex function. Then what you need to know is that f (.) is convex and the norm is convex. Here any norm is ok, because of …

It's more correct to say that he proved Jensen's Inequality (with arbitrary real weights) for functions which are midpoint convex and continuous. Of course, Jensen's Inequality with two …

Aug 29, 2020 · For the definition of convexity, the graphical perspective is that the line joining any two points is always above the region of the function values in between these points. what …

Jan 10, 2017 · Why you taking derivatives ? Write down the definition of strong-convexity without using assuming / gradients. Let the modulus of convexity tend to zero; you obtain the definition …

Jun 3, 2020 · There is a general topology flavoured definition of a general convexity space, which generalises the already existing notions of convexity that have been defined in the past.

Aug 16, 2019 · 21 What you gave is the standard definition of a convex function. If f is supposed to be continuous, it is enough to check that f (x + y 2) ≤ f(x) + f(y) 2 for all x, y. If f is twice …

It is well known that one equivalent definition of convexity is the statement that the gradient of secant lines increase. One way to write this down is as follows: for all $x<y<z$,