Reducing monomials after an optimization.

[JOlucak]

In the Appendix of Tan's disseration he mentions to check the magnitude of the coefficients after the optimization. If some of them are five/six magnitudes smaller compared to the others you can most likely get rid of them, i.e., remove the corresponding monomials from the monomials list and hence reduce the problem size.

I tried that by applying that as follows:

Assume a poly to be a gram polynomial, poly is one of the decision variable and we solved an SOS optimization problem.

[coeffs, monom] = poly2basis(poly);

% check the coeffs and then remove the monomials with small numerical values i.e. below magn.

[~, monom_reduced] = poly2basis( cleanpoly( poly, magn) );

% set up new poly with reduced number of monomials
s = casos.PS.sym('s',mon_reduced,'gram');

If I set up the new solver, an error is thrown because no gram basis could be found.

Two questions:
1.) Could the procedure from Tan be somehow automized?
2.) Is it normal to get the error message for the new setup? If so I would simply add it as a linear decision variable and a SOS constraint.