Nonlinear constrained vector optimization using Optimization Toolbox
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I am attempting to reproduce a nonlinear constrained vector optimization result obtained in Heuett/Qian (2006) using the fmincon solver's SQP algorithm in the Optimization Toolbox.
The general optimization problem is given by
and the specific objective function of interest in this case is given by
where J, J+ , J-, Jext, and delta_mu are all vectors, Jext_D is an element of vector Jext, and S and K^T are matrices supplied by the nature of the system in question.
I have coded the objective function in heuett_simple.m:
function f = heuett_simple(J_ext, delta_mu)
f = J_ext(4) + dot(delta_mu)/2;
end
since Jext_D will be the fourth element of the vector J_ext
and the constraints in heuett_constraints.m:
function [c, ceq] = heuett_constraints(J, J_plus, J_minus, J_ext, delta_mu)
model = sbmlimport('heuett_simple.xml');
S = getstoichmatrix(model);
S = full(S);
K = [-0.7163, -0.3345;
-0.3205, -0.4347;
0.4710, -0.6349;
-0.3958, 0.1001;
-0.0752, 0.5348];
c = [];
ceq(1) = S*J + J_ext;
ceq(2) = transpose(K)*delta_mu;
ceq(3) = diag(exp(delta_mu))*J_plus - J_minus;
ceq(4) = J - J_plus + J_minus;
end
The specifications of model, S, and K are specific to the problem I am working on. S is a 4x5 matrix of type double. When I execute this problem using the Toolbox with the following setup (without bounds for the time being)
I receive the error
Index exceeds matrix dimensions.
Any idea what is causing my problem?
2 Comments
Ingrid Tigges
on 16 Sep 2014
Would it be possible for you to provide a reproduction example? This helps answering this kind of questions a lot.
Answers (2)
Sean de Wolski
on 16 Sep 2014
>>dbstop if error
Then run the code. This will stop on the line throwing the error and you can look at the index v. the size of your matrix and see what's happening.
4 Comments
Matt J
on 16 Sep 2014
Edited: Matt J
on 16 Sep 2014
I suppose that this is because I am supplying an element of a vector in the objective function -- J_ext(4).
@Sam,
You still haven't followed Sean's advice about using dbstop. Had you done so, there would be nothing to "suppose". The program would pause at line 2 in heuett_simple() and you could show us directly what J_ext contains.
Matt J
on 16 Sep 2014
One of the errors you have is that you are feeding the unknowns to the objective function and constraints in multiple input arguments, e.g.,
function f = heuett_simple(J_ext, delta_mu)
f = J_ext(4) + dot(delta_mu)/2;
end
All the unknowns must be fed in as a a single variable, like in the following
function f = heuett_simple(unknowns)
J_ext=unknowns(1:N);
delta_mu=unknowns(N+1:end);
f = J_ext(4) + dot(delta_mu)/2;
end
and similarly with your constraints.
1 Comment
Matt J
on 16 Sep 2014
Another error is that you have selected an initial point [0,0] consisting of only 2 elements, when you apparently have considerably more than 2 unknowns.
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