I use fmincon to minimise weight to stiffness ratio. This ratio is Non linear. I tested this solver by using different initial points Xo. However, results are changeable and dependent on Xo.
I am afraid that solver cannot be suitable for such system of equations.
Have you checked whether it is a convex problem? It probably is not, whence your algorithm may give responses based on where you start the procedure. Move on to global methods to see where the minimum lies - if there is one.
check the convexity of your problem. if not convex then this is another story.
Fmincon can not help you. Fmincon is based on interior point method. This means that if the function convex, then any initial point result to the optimal. if not convex then the space is so complicated and the solution depends on the initial point and of course the global solution can not be guaranteed.
Please send it to me may be I can help you
Up till today, there is no theoretical or practical proof that any kind optimization method is 100% capable of finding the global optimum for a generic problem. Unless you have a special type of problem eg a simple convex function, like it was mentioned before then it is the expected behaviour. This is where your skills/intuition/understanding of the problem comes into play, to influence the initial conditions to help you find your global optimum.
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