Finding an initial feasible point x0 for fmincon

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.

Answer 1

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:

http://www.mathworks.com/help/optim/ug/when-the-solver-fails.html#br44i73

"You can set your objective function to zero keeping constraints as it is and run the optimization to find a new feasible start point."

Even by keeping the objective function zero, fmincon still requires an x0 too, right? Which x0 would I use there?

Did you get an opportunity to read the link? They explain a two step process to first a point that satisfies linear constraints and then use that to find a point that satisfies non linear constraints. I recommend you go through the whole page, which will also answer questions you may have in the future. As Matt J mentioned it is not absolutely necessary that you choose a feasible point but helps to do so.

Answer 2

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.