minimize

minimize(const Function<real(List)> f, Map options) -> Map

Performs nonlinear minimization of a real function with either gradient or gradient-free algorithms.

Minimizes a real scalar objective function.Handles both gradient and gradient-free optimization depending on the algorithm used.

Parameters

• f: The objective function to minimize. Must be a real function of the form $f(x)$ where $x$ is a List of real numbers $[x_0,\dots,x_{D-1} ]$ where $D$ is the dimension the function domain.
• options: Map containing optimization settings.
  • grad (Function<List<real>(List<real>)>): gradient function of $f$ to be used for gradient based algorithms.
  • x_init (List<real>): initial parameter guess.
  • algorithm (string): specifying the optimization algorithm to use.
  • lb (List<real>): lower bounds on input domain.
  • ub (List<real>): upper bounds on input domain
  • xtol (real): numerical error tolerance of the solution (default 1e-6).
  • ftol (real): numerical error tolerance in the minimum funciton value (default 1e-6).
  • max_eval (integer): maximum number of function evaluations.

Returns

Map containing optimization results.

Example

// Minimize the rodenbrock funciton
def rosenbrock(List x) {
    var a = 1.0 - x[0]
    var b = x[1] - x[0] * x[0]

    return a*a + 100.0 * b*b
}

var options = ["algorithm": "LN_NELDERMEAD", 
                "x_init": [-1.0,-2.0] ,
                "lb": [-5.0,-2.0], 
                "ub": [5.0,5.0] , 
                "xtol": 1e-8 , 
                "ftol": 1e-8]

var result = minimize(rosenbrock, options)

print(result)