## How to use fminunc to solve simultaneous system of equations?

### Ash Ash (view profile)

on 13 Jul 2018
Latest activity Commented on by Matt J

### Matt J (view profile)

on 14 Jul 2018
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.

#### 1 Comment

Kaushik Lakshminarasimhan

### Kaushik Lakshminarasimhan (view profile)

on 13 Jul 2018
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.

### Matt J (view profile)

on 14 Jul 2018

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

### Walter Roberson (view profile)

on 14 Jul 2018
fsolve() looks for simultaneous zeros, but the user wants to minimize.
Matt J

### Matt J (view profile)

on 14 Jul 2018
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