No solution with fsolve. Why do fsolve stop before doing any iterations?

I have a system with 7 Equations and 7 variables. I think the system should be solvable, but there might be misspecifications I have overlooked(I have tried for days). When trying to solve matlab tells me that the system is without a solution before preforming any iterations. Display Message:

                                       Norm of      First-order   Trust-region
 Iteration  Func-count     f(x)          step         optimality    radius
     0          8         25.9606                             0               1

fsolve stopped because the sum of squared function values, r, has gradient with
relative norm 0.000000e+00; this is less than options.TolFun = 1.000000e-01.
However, r = 2.596059e+01, exceeds sqrt(options.TolFun) = 3.162278e-01.

So the solution stops before doing iterations. Why is this and how do I fix it?

I have attetched the m-files, but they are a bit messy. Pasting the main features bellow. Call file:

x0 = [1.0 , 1.0 , 0.5 , 1.5 , 1.5 , 0.5 , 0.1]; 
options=optimset('Display', 'iter-detailed', 'Diagnostics', 'on' );   
[z,fval,exitflag,output] = fsolve(@testsig,x0,options)
Function:

Function:

function G = sig(x)
global in1 in1f beta tauf l lf y yf B rr d PY aa h c b p
% Inputs from 1: y, yf, d, l, lf
x = zeros(7,1);
G = zeros(size(x));
G(1) = 1/(1+x(7)) - beta*x(1)*sum(((1-d)./(y-(1+x(7)).*(1-d)*B+(1+x(7)).*(1-d)*x(3)-l+(1+rr)*x(4))).*PY);
G(2) = 1/(1+rr) - beta*x(1)*sum((1./(y-(1+x(7)).*(1-d)*B+(1+x(7)).*(1-d)*x(3)-l+(1+rr)*x(4))).*PY);
G(3) = x(1) + x(3) + x(4) - in1;
G(4) = 1/(1+x(7)) - beta*x(2)*sum(((1-d)./(yf -tauf+(1+x(3)).*(1-d)*x(5)-lf+(1+rr)*x(6))).*PY);
G(5) = 1/(1+rr) - beta*x(2)*sum((1./(yf -tauf+(1+x(3)).*(1-d)*x(5)-lf+(1+rr)*x(6))).*PY);
G(6) = x(2) + x(5) + x(6) - in1f;
G(7) = B - x(3) - x(5);

All help is appreciated!

Answer 1

[Alan Weiss]

The gradient of your function is zero at x0. Perhaps you can start at a different point, or double-check that your "sig" function is doing what you think it should be doing. See the suggestions on what to do when fsolve fails.

Alan Weiss

MATLAB mathematical toolbox documentation

[Nicolai]

Thanks,

I have tried a lot of starting Points all around the feasible values. So I think there must be something wrong With the specification of the function, but I can't figure out what.

How do matlab calculate the gradient? The "gradient(F)" option Returns a non zero vector. would be helpful for the debugging process.