Is it possible to minimise a multi variate sym function without any iterative method in MATLAB?

I have a sym function, say F which is a 100x1sym containing three symbols x,y and z in it. I am not interested in using the lsqnonlin or fmincon commands in MATLAB. I would like to use the analytical method. i.e finding out the first derivative of a function and equating it to zero. So, Is it possible to find the optimal value of x,y and z so that the sym F is minimum without an iterative method.

My approach:

• Since there are three variables, I found out the jacobian of any three rows in the 100x1 sym F
• I tried to solve by equating the Jacobians of above found out three rows to zero , thinking that a function is minimum if its first derivative is zero. But whenever I solve this, I tend to get 0 as values.

So It would be kind If I get to know whether there is some fallacy in my thought process.

Thanks in Advance Quicklearner.

[Torsten]

So you want to minimize

sum_{i=1}^{100} F(i)^2

where the F(i) depend on three parameters x,y and z ?

Best wishes

Torsten.

[quicklearner]

Yes Torsten, you are right.

[Torsten]

ok, then you must consider the function

G(x,y,z)=sum_{i=1}^{100} F(i)^2

calculate dG/dx, dG/dy and dG/dz (thus the Jacobian of G) and set the resulting expressions to zero.

This will usually give you a system of three nonlinear equations to solve.

If you are lucky (but I doubt), the equations can be solved for x,y,z in an analytical way.

Best wishes

Torsten.