Which function can I use instead of fsolve to solve a system of nonlinear equations with a global optimisation?
I am trying to solve 3 non linear equations and I cannot have good guess values for those equations. I read along different documents, that the solution my be to use global optimisation functions instead of local optimisation ones, as fsolve.
However, I am not very familiar with these functions (fminunc,patternsearch,ga …)
Could anyone help me with that?
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First of all, mathematical theory tells us that there exist functions where knowing the value of the function at one location gives you no information about the value of the function at any other location. It follows from this that there exist nonlinear equations which cannot be solved by any gradient descent, or genetic algorithm (that does not run all possibilities exhaustively), or newton’s method, or simplex method, or anything else implemented by the functions you list — not short of flailing around and happening to try an exact solution by chance.
Second of all: when you have “black box” functions (a function handle for code you are not permitted to examine analytically) then it can be quite difficult to find solutions of equations even when clear solutions exist analytically. Therefore none of the functions you list can guarantee solutions to global minima or to nonlinear equations — not outside of certain narrow classes of functions.
Third: Every equation f(x) == b has an equivalent minimization problem norm(f(x)-b) with the equation being solved at the locations where that norm is 0, and the equation being hopefully solved to within accuracy and round-off error where the norm is minimized if no exact zero can be found. For real-valued functions, the norm squared can be substituted, (f(x)-b).² .
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