finding stable point for complicated contrained function - tried ga

Hello,

I have function with two variables and a few parameters:

function [delta] = fun(x,par)

... %does a lot of things
    
delta=abs(delta) %I use abs() since ga looks for minimum, not root, as I understand
%this is the last line of the function and prints to output for my testing,
%see below

I want to find the stable points aka where delta(1)==0 & delta(2)==0 for a given set of parameters.

x shall be restricted to 0 <= x(1) <= 1 and to 1-x(1)(1-x(1))*2 <= x(2) <= 1

I am not familiar enough with search and solve algorithms to understand which one would work for my function and my problem. I could even make it work with fsolve, just by brute force with many starting conditions and excluding the solutions outside the restrained area after the fact ... but of course that's quite shit and it still fails sometimes.

I wanted to try the genetic algorithm.

Since x(1)<=1, -x(1)<=0 and x(2)<=1 I would use (I guess for x(1) I could use lb and ub instead, right?)

A=[1,0;-1,0;0,1];b=[1,0,1];

and since 1-x(1)(1-x(1))*2 <= x(2) I would use

function [c,ceq] = nonLinConstrain(x)
c = (1-x(1)*(1-x(1))*2) - x(2);
ceq=[];

I first tried to run it with fixed parameters (basically without parameters)

function [delta] = fun(x,par)
if nargin<2
    par=blabla;
end
...

using the command

x = ga(@fun,2,A,b,[],[],[],[],@nonLinConstrain);

But even here I get an error, which I can't quite understand. It seems to fail after receiving outputs for the second time

delta =

0.1000 0.1800

delta =

0.1000 0.1800

Error using makeState (line 67)

Your fitness function must return a scalar value.

Error in gacon (line 54)

state = makeState(GenomeLength,SubFitness,Iterate,subtype,options);

Error in ga (line 418)

[x,fval,exitFlag,output,population,scores] = gacon(FitnessFcn,nvars, ...

I would appreciate tips concerning

1) Why this won't run?

2) How to use changing parameters with ga

3) If I should try other solvers?

Thank to you all!

[Star Strider]

Here:

function [delta] = fun(x,par)

the value for ‘delta’ needs to be a scalar.

There is not enough information to provide a more detailed solution.