My cost function is the sum of squares of all nC2 pairs of output i.e.
F(X) = SUM (i = 1 to N) [ SUM(j= i+1 to N) [ (xi*xj)^2]]
I have been trying to optimize it with CVX pertaining to some constraints. However, I am skeptical whether such a function is convex or concave?
A slight idea would help a lot.
Help will be very appreciated.
Thanks
Sidharth
This is not convex.
Let N = 2. then F(X) = x1*x2, which is indefinite, i.e., neither convex nor concave.
You should read the FAQ FAQ: Why doesn’t CVX accept my problem? [READ THIS FIRST] .
Let me paraphrase from the FAQ): if you do not know whether or not your problem is convex, you should not be using CVX.
But yeah, it’s neither convex nor concave, as can easily be seen by looking at the Hessian for N=2, in which case F(X) = x1^2 * x2^2, whose Hessian can be either positive semi-definite or indefinite, depending on the values of x1 and x2.