Hi guys,

I have now found the solution to the problem. The DirectSearch is definitely a valid solver, however due to the high solution time of this solver I used the regular fsolve and factorized the roots out of the polynomial, thus the solver is forced to find another root.
With that being said I also needed to deal with some spurious roots originating from the formulation of the problem.

Thank you for all your answers. They have been most helpful :-)