How to use fminunc to solve simultaneous system of equations?

Hi, I am looking to minimise a system of multivariate underconstrained simultaneous equations using fminunc, with 5 variables and 20 equations, which are all generated in a symbolic form because the equations will vary based on inputs.

Firstly I have figured out how to solve one example equation using fminunc:

x=sym('x',[2,1]);y=sym('y',[3,1]);
eqn=3*x(1)^2 + 2*x(1)*x(2) + x(2)^2 - 4*x(1) + 5*x(2);
fun = matlabFunction(eqn) ;
funMiddleMan = @(y) fun(y(1),y(2));
sol = fminunc(funMiddleMan, [1,1])

The problem I am faced with now, is how do I repeat this for multiple equations?

x=sym('x',[2,1]);y=sym('y',[3,1]);
eqn(1)=3*x(1)^2 + 2*x(1)*x(2) + x(2)^2 - 4*x(1) + 5*x(2);
eqn(2)=3*x(1)^2 + 2*x(1)*x(2) + x(2)^2 - 2*x(1) + 4*x(2);
fun = matlabFunction(eqn) ;
funMiddleMan = @(y) fun(y(1),y(2));
sol_2 = fminunc(funMiddleMan, [1,1])

I tried the script below and it gave me the following error

Error using fminunc (line 346)
Supplied objective function must return a scalar value.

Could you please help me? Thank you.

[Kaushik Lakshminarasimhan]

What is it that you are trying to minimize? You have two equations, so your funMiddleMan returns two outputs instead of one. You need to reformulate your objective so that funMiddleMan returns a scalar value.

Answer 1

[Matt J]

Use FSOLVE instead of FMINUNC. It is better tailored to this specific type of problem. Also, you do not have to scalarize the objective function with FSOLVE, so it will mean less code modification for you.

[Walter Roberson]

fsolve() looks for simultaneous zeros, but the user wants to minimize.

[Matt J]

I'm working on a hunch that that's not what the OP really wants. fsolve() will still try to minimize the norm of the objective if simultaneous zeros cannot be found

Answer 2

[Walter Roberson]

To minimize a system of equations, you need to use gamultiobj(), which will build pareto fronts.

https://www.mathworks.com/help/gads/pareto-front-for-two-objectives.html