unconstrained nonlinear optimization problem
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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
5 个评论
Why fmincon? You have no constraints. You probably should add some constraints, however, because the solution is currently not unique. Since the objective depends only on the differences 
, adding any constant to any optimal 
will produce another optimal solution.
, adding any constant to any optimal will produce another optimal solution.
Bjorn Gustavsson
2020-10-16
Why isn't 
for all i a solution? Shouldn't that make every term in the sum zero, and that ought to be the smallest possible value...
for all i a solution? Shouldn't that make every term in the sum zero, and that ought to be the smallest possible value...
John D'Errico
2020-10-16
编辑：John D'Errico
2020-10-16
And why would you bother to use fmincon to minimize a function that can be solved using multiple linear regression in the first place?
Not only are you wanting to use a Mack truck to carry a pea to Boston, but you never even needed any truck at all. A bycycle would suffice.
And as Bjorn points out, a trivial solution exists anyway.
Heborvi
2020-10-16
采纳的回答
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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