How write these equation in Matlab for optimization

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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

Accepted Answer

Thiago Henrique Gomes Lobato
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.
Thiago Henrique Gomes Lobato
You have this already. Note that you divide by sum(x). This is a linear operation, so it would be the same as:
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.

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