MATLAB: Fsolve to solve 5th order polynomial

fsolvefzeromathematics

I would like to solve the following polynomial numerically for r:

I am trying to use fzero as follows:

r= (5/(r^2*9))- ((2)/(9*(6-r)^2))
x0 = 10; % some initial point
x = fzero(r,x0)

How can this be solved using fzero?

This works.

fun=@(r) (5/(r^2*9))- ((2)/(9*(6-r)^2))-r;
x0 = 10; % some initial point
x = fsolve(fun,x0)

E.g., 5th Order Runge-Kutta-Fehlberg coefficients can be found here:

The error is straightforward:

Error using fmincon (line 635)
Supplied objective function must return a scalar value.

This is the reason fsolve works, since it is a root-finding algorithm.

In order for this to work with fmincon (and certain other optimisation functions), you would need to do something like this:

[x,fval,exitflag,output] = fmincon(@(x)norm(Obj_Fun(x)),x0,A,b,Aeq,beq,lb,ub)

That will llikely work with fmincon. Whether it produces the desired result is less certain.