unconstrained nonlinear optimization problem

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Heborvi
Heborvi 2020-10-16
编辑： Matt J 2020-10-16
Hello,
Kindly I have a question concerning nonlinear optimization problem. I have the following problem:
How I can define this objective function in matlab?
Thank you
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Matt J
Matt J 2020-10-16
编辑：Matt J 2020-10-16
I think Bjorn mean's . The solution set is for any scalar constant c.
Heborvi
Heborvi 2020-10-16
Thank you for your replies and I am sorry because there is an error in writing the optimization problem. the problem is the diference between d_{ij} and the euclidean distance between vectors. I have changed it in the question.

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Matt J
Matt J 2020-10-16
编辑：Matt J 2020-10-16
Still, there are no constraints, so I think you should be using fminunc. Also, your revised objective function is not differentiable near theta=X, so you'll have to hope that the optimizer doesn't search there.
N=nchoosek(n,2);
I=1:N;
J=nchoosek(1:n,2);
C=(sparse(I,J(:,1),1,N,n)+sparse(I,J(:,2),-1,N,n)).';
thetaOptimal=fminunc(@(theta) P(theta,X,C,d), theta0);
function fval=P(theta,X,C,d)
%theta - pxn matrix of unknowns
% X - known pxn matrix
% d - column vector of length nchoosek(n,2)
V=vecnorm((X-theta)*C,2,1);
fval=norm(d-V(:)).^2;
end

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