lsqnonlin optimization: large condition number of Jacobian matrix at all iterations, but full rank
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Well, there's nothing enforcing your convexity constraint at the moment. So, whether you include them or not doesn't seem to make a difference.
The constraints on the parameters are implemented in A*x<b. A and b are passed to lsqnonlin. Some (not all) rows of A depend on x(2) and x(9).
If you have a PDE to satisfy, I think it should be implemented as a nonlinear constraint.
Maybe worth do try that in the future. I agree with you that probably the pde solver is the bottleneck currently.
Just shortly: if I can manage to implement my pde as a nonlinear conatraint, what is the purpose of the objective function then? Right now, the objective is called with a point in parameter space and the pde solver returns gsim and J at that point. But if the pde solver is not there anymore, how do I feed lsqnonlin with gsim and J?
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