[Help-gsl] Re: Simulated Annealing for a system of 9 equation, 5 unknowns

[Doug McKee]

> This system is very nonlinear and I have tested Newton’s method to  
> solve it but I converge not necessarily on the true solution  
> because it seems truly to depend of the initialization of my unknown.
> So, I have find the Simulated annealing to find the global minimum  
> and the true solution but in the test.c of siman program I have  
> just view an example of one equation with many unknown and not an  
> example of a system of equation with many unknown.
>
> My question is how can I use this program with my system of equation?

You just need to compose an objective function that corresponds to  
zero if all the equations are satisfied.  Suppose your system looked  
like this where both f() and g() depend on a set of parameters theta:

f(x,y) = a
g(x,y) = b

Your objective function should be something like

        F(theta) = ( f(x,y) - a)^2 + ( g(x,y) - b)^2)

Then you just use the anneallor to minimize F() to get a solution.

Doug

-------------------
Doug McKee
address@hidden
http://dmckee.bol.ucla.edu
310-266-2438