fsolve, fmincon producing different results

Hi,

I am wondering how to think about fsolve and fmincon producing different results when solving the same system of nonlinear equations. To explain, fsolve finds a solution that sets x, y, z simultaneouly to zero when x, y, z are some equations.

To run the same routine in fmincon, I set the objective as [x y z]*[x y z]' to be minimized (tolerance 1e-15). And these two routines produce very different solutions, even when they start from the same initial value.

Is it the way I set the objective in fmincon that is wrong or leads to a different solution? How should I think about this? Thanks for any advice in advance!

Best,

Ara

Answer 1

[Matt J]

Do they both achieve the same objective value? If so, you simply have multiple solutions.

Answer 2

[Sargondjani]

I believe fmincon could also be stuck in a local minimum, due to the quadratic terms. This solution might not actually solve the equations.

And in addition to what Matt says: if you start fmincon from a point close to the solution of fsolve, does it converge to the same point then?

On a side note:

• do you need fminconsince you have no constraint. Maybe fminunc suffices?
• lsqnonlin is a special function to minimize vector valued functions in least square sense. It can also handle bounds, so this might be useful too.