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 functionlog(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) -(wTl– 1)

Any ideas?

I have attached a word document which explaines better.