matlab fminunc

fminunc is a function in MATLAB that computes the unconstrained minimum of a scalar function. It uses the gradient of the function to find the minimum.

Syntax:
[x,fval,exitflag,output] = fminunc(fun,x0,options)

where:
- fun: the function handle to the objective function
- x0: the initial guess for the minimum
- options: a structure that specifies the options for the optimization algorithm
- x: the minimum found by the algorithm
- fval: the value of the objective function at the minimum
- exitflag: a flag that indicates whether the algorithm converged to a solution or not
- output: a structure that contains information about the optimization process

Example:

Suppose we want to find the minimum of the function f(x) = x^2 + 2x + 1. We can define the function handle as follows:

fun = @(x) x^2 + 2*x + 1;

We can then use fminunc to find the minimum:

[x,fval,exitflag,output] = fminunc(fun,-5);

The output will be:
x = -1.0000
fval = 0
exitflag = 1
output =

struct with fields:

iterations: 3
funcCount: 12
stepsize_min: 1.0000e-08
cg: [1x1 struct]
message: 'Optimization terminated: gradient small enough to continue searching for solutions.'

This indicates that the minimum is -1, the value of the function at the minimum is 0, and the algorithm converged to a solution.