fsolve for 2 equation with 2 variables

Here is my function, in order to shorten the expression here I add A and B, but in my original function they are inside F(1) and F(2) (i.e. that is not the problem), this is the error I get: Objective function is returning undefined values at initial point.

function F = myfun(x)
N=32;
K=5;
s=1;
b=0.1;
P=5;
A=-2*s^4*x(1)*N+2*s^4*x(1)*K+3*s^2*x(2)*log(2);
B=sqrt(8)*x(2)*s^2*log(2);
g=exprnd(1,1,N-K); 
F(1) = sum((g.*(1-b*x(1))/(x(2)*log(2)))-1./g)+(N-K)*((A+sqrt(A^2-B^2))/((4*s^2/sqrt(8))*B))-N*P;
F(2) = b*(sum(log2((g*(1-b*x(1)/x(2)*log(2))))))-(N-K)*log2(1+(2*A^2+2*A*sqrt(A^2-B^2)-B^2)/((4/sqrt(8))*B*(A+(4/sqrt(8))*B+sqrt(A^2-B^2))));
end

Answer 1

[Star Strider]

What is the initial point you chose? Your function returns finite values for random non-zero arguments. It returns [NaN NaN] for [0 0] as an input.

The solution is most likely to use an initial point other than [0 0]. I would use rand(2,1).

[Miroslav Mitev]

Thank you, you are right. Just one last thing, do you know how can I add constraints on x1 and x2 and how can I get all the iterations?

[Star Strider]

My pleasure.

See the documentation for the Optimization Toolbox fmincon (link) function. It will allow you to specify many types of constraints.

[Miroslav Mitev]

Actually when I set

x0=rand(2,1);
example (0.3211 0.5321)

and when I enter

fsolve(@myfun,x0)

it returns me the same values

 (0.3211 0.5321)

as a solution, which can not be true.

[Star Strider]

Your function may not have a solution either using the root-finding function fsolve or the minimisation functions like fmincon. I got equivocal or inconsistent results for both.

[Miroslav Mitev]

There is a solution for sure it is just a bit complicated expression. I am still not sure how to get the result, but anyway, your answer is helpful, thank you

[Matt J]

Since it is only a function of 2 variables, you could do a coarse surf() plot of norm(F) and find visually where the roots approximately lie. This would give you a better initial guess than simply randomizing.

[Star Strider]

My pleasure.

It might be useful for you to post the symbolic expression you are coding as well as your code for it as a new Question, since that seems to be the problem.