How to fit a generate polynomial coefficients of with general requirements

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Alec Reed
Alec Reed on 11 Oct 2021
Commented: Alan Weiss on 11 Oct 2021
Hi I am attempting implicitly describe a state space using a polynomial where any point in the state space results in the polynomial being negative, otherwise it should be positive. I might have formulated the problem incorrectly so apollogies in advance.
I need to find the coeffiencents of the following 4 variable polynomial (10 total r_i's):
find
s.t.
Its kind of like curve fitting, but I dont actuall have any data points. I would appreciate anyone helping point me in the correct direction or even what this kind of optimization is called.

Answers (1)

Alan Weiss
Alan Weiss on 11 Oct 2021
I could be wrong, but it sounds to me as if the Problem-Based Optimization Workflow would work well for you. You do not have an objective function, you simply have bounds and constraints. If you set up your problem and variables with the appropriate bounds and constraints, then call solve, you should get back a feasible point.
Is that what you are looking for?
Alan Weiss
MATLAB mathematical toolbox documentation
  2 Comments
Alan Weiss
Alan Weiss on 11 Oct 2021
Hmm, maybe the fseminf solver is somehow relevant. That solver has semi-infinite constraints.
Good luck,
Alan Weiss
MATLAB mathematical toolbox documentation

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