cmss Using the first differential

Fortunately, when a function, like above, is differentiable, more efficient optimization algorithms can be used. If minimize() is given the differential of the optimized function, using the "df" option, it will use a conjugate gradient method.

## Function returning partial derivatives

function dc = diffoo (x)

    x = x(:)' - 1;

    dc = sin (x) + 2*x/9;

endfunction

[x, v, n] = minimize ("foo", x0, "df", "diffoo")

This produces the output :

x =

  1.00000 1.00000 1.00000

v = -3 

n =

  108 6

The same minimum has been found, but only 108 function evaluations were needed, together with 6 evaluations of the differential. Here, diffoo() takes the same argument as foo() and returns the partial derivatives of with respect to the corresponding variables. It doesn't matter if it returns a row or column vector or a matrix, as long as the element of diffoo(x) is the partial derivative of with respect to .