I am basically using a Lagrange technique to optimise a portfolio of 5 assets, with conditions that the weights must add up to one, and a utility function. I can explain in more depth where these constraint scome from if it helps, but I think if you see the Maths thats all thats need to be solved really.
How to use utility function log(x/ ym ) to obtain the optimal portfolio where m is a number (usually >1)
Introduce Lagrange multiplier
Now x and y are vectors too, and I am ultimately trying to find w.
L = log(x ) – m log(y ) - (wT l – 1)
I have attached a word document which explaines better.