Double summation with multiplication

Hi there, I currently working on a my study's final project One of which require me to solve this kind of equation

Objective is to maximize this function

r, sigma(i) --> for standard deviation, teta, and cov(i,j) are known number and I want to find the w(i) value with constraint: - Lower bound for w(i) is 0 - Upper bound for w(i) is 0 - Sum w(i) is 1

Any help is very appreciated and sorry for bad english

Answer 1

[Walter Roberson]

To maximize something, minimize its negative. You can use fmincon for that, using a lowerbound.

Although it might seem most natural to code sum(w)=1 as a linear equality constraint, that form is inefficient because it can take a lot of hunting to fit the equality. Instead use one fewer w, calculate the last w(i) as 1 minus sum(w(1:i-1)), and have a linear inequality constraint on sum(1:i-1) as being < 1 (strictly) so that there always some room for the last w(i)