Selection of Proper Optimization Function for Finding Global Minimum

I am currently working on the following optimization problem and want to ensure I am getting the global minimum. I am not familiar with optimization functions, so am not sure which algorithm is most appropriate for me. I have access to the Global Optimization Toolbox. The objective function is written as such:

function e2 = IOT_objective(r)
    %want to minimize e2
    % r --> A row vector with a size of 1 x n
    % S --> matrix with a size of n x m
    % dm --> A row vector with a size of 1 x m
    e=dm-r*S;
    e2=e*e';
end

Answer 1

[Matt J]

If r is the only unknown, then your objective is convex. Assuming your constraints are also convex, any solution will be a global minimum.

[Adam Rish]

My constraints are that all elements must exist between 0 and 1 and sum of r=1

[Matt J]

So, you can od this with lsqlin(), like we discussed in your previous post,

https://www.mathworks.com/matlabcentral/answers/800241-writing-minimization-function-to-find-multiple-vectors?s_tid=srchtitle

[Adam Rish]

Awesome thank you!