On ℋn+1-convex functions: asymptotic behaviour and subdifferentials. (3rd April 2019) - Sheykhi, A.; Doagooei, A. R.
Abstract: First, we show thatH n + 1, the class of functions defined as the point-wise minimum of n +1 affine functions defined on the Euclidean spaceR n, has the peaking property. Then we characterizeH n + 1 -convex functions by means of asymptotic cones and asymptotic functions. Finally, some conditions in order to guarantee the nonemptiness of subdifferentials ofH n + 1 -convex functions are established.