I have a problem to express sum_{i,j} {x[i][j]^(a+1)/w[i]^a} where x and w are non-negative variables, and a is a non-negative rational number. I checked that this is convex.

If a = 1, I can express it using a Quadratic_over_lin function. I cannot generalize it.

I tried to express it using Power cone, however, it does not work because w[i] is inter-related to all x[i][j]. Is there any way to express this function?

Thank you.