fminunc

Find the unconstrained minimum of a real function.

Syntax

x = fminunc(@func,x0)

x = fminunc(@func,x0,options)

[x,fval,info,output] = fminunc(...)

Inputs

func
The function to minimize. See the optimset option GradObj for details.
x0
An estimate of the location of the minimum.
options
A struct containing option settings.
See optimset for details.

Outputs

x
The location of the function minimum.
fval
The minimum of the function.
info
The convergence status flag.
info = 4
Relative step size converged to within tolX.
info = 3
Relative function value converged to within tolFun.
info = 2
Step size converged to within tolX.
info = 1
Function value converged to within tolFun.
info = 0
Reached maximum number of iterations or function calls, or the algorithm aborted because it was not converging.
info = -3
Trust region became too small to continue.
output
A struct containing iteration details. The members are as follows:
iterations
The number of iterations.
nfev
The number of function evaluations.
xiter
The candidate solution at each iteration.
fvaliter
The objective function value at each iteration.

Examples

Minimize the Rosenbrock function.
function obj = Rosenbrock(x)
obj = (1 - x(1))^2 + 100 * (x(2) - x(1)^2)^2;
end

x0 = [-1.2, 1.0];
[x,fval] = fminunc(@Rosenbrock, x0)
x = [Matrix] 1 x 2
1.00000  1.00000
fval = 1.29122e-15
Modify the previous example to pass an extra parameter to the function using a function handle.
function obj = Rosenbrock2(x, offset)
obj = (1 - x(1))^2 + 100 * (x(2) - x(1)^2)^2 + offset;
end

handle = @(x) Rosenbrock2(x, 2);
[x,fval] = fminunc(handle, x0)
x = [Matrix] 1 x 2
0.99999  0.99999
fval = 2

fminunc uses a quasi-Netwon algorithm with damped BFGS updates and a trust region method.

Options for convergence tolerance controls and analytical derivatives are specified with optimset.

To pass additional parameters to a function argument, use an anonymous function.

The optimset options and defaults are as follows:
• MaxIter: 400
• MaxFunEvals: 1,000,000
• TolFun: 1.0e-7
• TolX: 1.0e-7