# How write these equation in Matlab for optimization

6 views (last 30 days)
Dear Friends,
I want to write this optimization problem in matlab.
Anybody here to help me write thi in Matlab please.
the only one decision variable is    First you don't need the variable w, your problem is to maximize corr(Q,S), which is a unconstrained problem in x. Second, by your problem definition, Q is a single value, and correlation between single values doesn't make much sense, so I believe what you mean by corr is that the values should be equal or Q is a vector and you forgot a summation index. Considering the second hypothesis an example of how to do it could be seen here:
% Random data
S = 1:100;
c = randn(100,4);1
% Function to minimize
f = @(x,S,c)-min(min((corrcoef(S', (x*c')/sum(x) )) )); % Negative so min = max. Two min's since corrcoef gives a matrix as output
% Minimizer
[x,fval] = fminsearch(@(x)f(x,S,c),[1,1,1,1])
You can use this code as basis to implement your problem.

Suppose the optimizer finds a value of -2 for a x entry. When it goes to the function the -2 becomes +2 because of the absolute. Which means that if you do
[x,fval] = fminsearch(@(x)f(x,S,c),[1,1,1,1])
x = abs(x);
You will still get the same cost function, i.e., the abs(x) is exact the same minimum.
Muhammad Usama on 5 Jul 2020
Thank you Sir.
one more thing, I want to add sum(x) ==1
is it possible?
You have this already. Note that you divide by sum(x). This is a linear operation, so it would be the same as:
(x/(sum(x)))*c'
which would give: sum(x) ==1. In other words, if you normalize x by it's sum you'll get the same result as the not normalized one.