Optimizes a function using the BFGS descent algorithm.


{ x, f, g, ret } = QNewton(&fct, start[, ...])
  • &fct (function pointer) – pointer to a procedure that computes the function to be minimized. This procedure must have at one input argument, a vector of parameter values, and one output argument, the value of the function evaluated at the input vector of parameter values. Additional optional arguments may be passed in to the objective function fct using dots (...).

  • start (Kx1 vector) – start values.

  • .. (any) – Optional. A variable number of extra arguments to pass to the user function. These arguments will be passed to the user function fct untouched.

  • x (Kx1 vector) – coefficients at the minimum of the function.

  • f (scalar) – value of function at minimum.

  • g (Kx1 vector) – gradient at the minimum of the function.

  • ret (scalar) –

    return code.

    0   normal convergence

    1   forced termination

    2   max iterations exceeded

    3   function calculation failed

    4   gradient calculation failed

    5   step length calculation failed

    6   function cannot be evaluated at initial parameter values

Global Input


(scalar), convergence tolerance for relative gradient of estimated coefficients. Default = 1e-5.


(scalar), pointer to a procedure that computes the gradient of the function with respect to the parameters. This procedure must have a single input argument, a Kx1 vector of parameter values, and a single output argument, a Kx1 vector of gradients of the function with respect to the parameters evaluated at the vector of parameter values. If _qn_GradProc is 0, QNewton() uses gradp().


(scalar), maximum number of iterations. Default = 1e+5. Termination can be forced by pressing C on the keyboard.


(scalar), if 1, print iteration information. Default = 0. Can be toggled during iterations by pressing P on the keyboard.


(Kx1 vector), labels for parameters.


(scalar), if 1, results are printed.


This example computes maximum likelihood coefficients and standard errors for a Tobit model:

/***qnewton.e - a Tobit model***/
// Get data
z = loadd("tobit");
b0 = { 1, 1, 1, 1 };
{ b, f, g, retcode } = qnewton(&lpr, b0);

// Covariance matrix of parameters
h = hessp(&lpr, b);
output file = qnewton.out reset;

print "Tobit Model";
print "coefficients standard errors";
print b~sqrt(diag(invpd(h)));

output off;

// Log-likelihood proc
proc lpr(b);
   local s, m, u;

   s = b[4];

   if s <= 1e-4;

   m = z[., 2:4]*b[1:3, .];
   u = z[., 1] ./= 0;

   retp(-sumc(u.*lnpdfmvn(z[., 1]-m, s) + (1-u).*(ln(cdfnc(m/sqrt(s))))));
Tobit Model
coefficients standard errors

  0.010417884 0.080220019
 -0.20805753  0.094551107
 -0.099749592 0.080006676
  0.65223067  0.099827309


If you are running in terminal mode, GAUSS will not see any input until you press ENTER. Pressing C on the keyboard will terminate iterations, and pressing P will toggle iteration output.

To reset global variables for this function to their default values, call QNewtonSet().