I have the following optimization problem and I am trying to check for its convexity.
link As per the definition of convexity, "a continuous twice differentiable function is convex ON a convex set, iff the hessian is positive semi definite on the interior of the convex set." The feasible region where I am trying to check for its convexity its convexity is defined by..
B, N, sigma are constants
B = 20000
N = 50
sigma = 3.7678e-17
w, p are variables(vectors of K elements)
w can vary from 1 to 50
p, 0 to 46 in dbm(unit of power..)
I have to convert in into watt before using it
p in watt = (10^(p in dbm/10))/1000.
The hessian comes out to be indefinite for MANY of the feasible points..But I am not sure if I am right. Is the problem CONVEX, can any one check please..?