How to find an initial feasible solution x0 for solving a minimization problem with non linear constraints (fmincon)?
For small problems, I can figure out an x0, but for big problems with many constraints that are not linear, I don't see how.
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It is not required that the initial point you choose be feasible.
It is simply helpful to the optimization that your initial guess be as close as possible to the global minimum. Making the initial guess close to your global solution is an art and not a science, and is also problem specific. We would need to see a mathematical description of the problem to advise anything.
You can set your objective function to zero keeping constraints as it is and run the optimization to find a new feasible start point.
This is explained in this link: