fmin
Syntax
fmin(f, X0, [fargs], [xtol=0.0001], [ftol=0.0001], [maxIter],
[maxFun])
Details
Use a Nelder-Mead simplex algorithm to find the minimum of function of one or more variables. This algorithm only uses function values, not derivatives or second derivatives.
Arguments
func is the objective function to be minimized. The function must return a numeric scalar.
X0 is a numeric scalar or vector indicating the initial guess.
xtol (optional) is a positive number specifying the absolute error in xopt between iterations that is acceptable for convergence. The default value is
ftol (optional) is a positive number specifying the absolute error in
func(xopt) between iterations that is acceptable for convergence. The default
value is 0.0001.
maxIter (optional) is a non-negative integer indicating the maximum number of iterations to perform.
maxFun (optional) is a non-negative integer indicating the maximum number of function evaluations to make.
It returns a dictionary with the following keys:
-
xopt: a vector of floating-point numbers, indicating parameter that minimizes function.
-
fopt: a floating-point number, indicating value of function at minimum:
fopt = f(xopt). -
iterations: an integer, indicating number of iterations performed.
-
fcalls: an integer, indicating number of function calls made.
-
warnFlag: an integer that takes the following values
-
0: Optimization algorithm completed.
-
1: Maximum number of function evaluations made.
-
2: Maximum number of iterations reached.
-
Examples
In the following example, we define a function f(x) and use the Nelder-Mead
simplex algorithm to find its minimum value.
def f(x) {return x*x}
fmin(f, 1)
/* Ouput:
xopt->[-8.881784197001252E-16]
fopt->7.888609052210119E-31
iterations->17
fcalls->34
warnFlag->0
*/