fmin

Syntax

fmin(f, X0, [fargs], [xtol=0.0001], [ftol=0.0001], [maxIter], [maxFun])

Arguments

f is the objective function to be minimized.

X0 is a numeric scalar or vector indicating the initial guess.

fargs (optional) is a tuple specifying the extra arguments passed to f for calling f(X, fargs...).

xtol (optional) is a floating-point number specifying the absolute error in xopt between iterations that is acceptable for convergence. The default value is 0.0001.

ftol (optional) is a floating-point number specifying the absolute error in f(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. The default value is the number of elements in X0 * 200.

maxFun (optional) is a non-negative integer indicating the maximum number of function evaluations to make. The default value is the number of elements in X0 * 200.

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.

It returns a dictionary with the following keys:

• xopt: Parameter that minimizes function.
• fopt: Value of function at minimum: fopt = f(xopt).
• iterations: Number of iterations performed.
• fcalls: Number of function calls made.
• warnFlag：
  • 0: Optimization algorithm completed.
  • 1: Maximum number of function evaluations made.
  • 2: Maximum number of iterations reached.

Examples

def f(x) {return x*x}
fmin(f, 1)

/* ouput:
xopt->[-8.881784197001252E-16]
fopt->7.888609052210119E-31
iterations->17
fcalls->34
warnFlag->0
*/

def targetFunc(x,y,z){
	return x*x+2*x*y+5*y+z
}

fmin(targetFunc,5,(11,4))

/* output:
fcalls->46
warnFlag->0
xopt->[-11.0000]
fopt->-62.0000
iterations->23
*/