How to fit a generate polynomial coefficients of with general requirements

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.

Answer 1

[Alan Weiss]

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

[Alec Reed]

I think I am better able to state that my problem is simply a polynomial design problem. I need to design a polynomial such that my variables are negative in the stated bounds. I think I am zeroing in on a potential solution path using the MATLAB addon YALMIP, which will allow me to generate polynomials given some set of contraints (it seems the contraints I am describing here are called "inifinate dimensional constraints").

Link to polynomial design section: https://yalmip.github.io/example/polynomialdesign/

Thank you!

[Alan Weiss]

Hmm, maybe the fseminf solver is somehow relevant. That solver has semi-infinite constraints.

Good luck,

Alan Weiss

MATLAB mathematical toolbox documentation