47.2 Functions and Variables for cobyla

Function: fmin_cobyla
    fmin_cobyla (F, X, Y)
    fmin_cobyla (F, X, Y, optional_args) ¶

Returns an approximate minimum of the expression F with respect to the variables X, subject to an optional set of constraints. Y is a list of initial guesses for X.

F must be ordinary expressions, not names of functions or lambda expressions.

optional_args represents additional arguments, specified as symbol = value. The optional arguments recognized are:

constraints

List of inequality and equality constraints that must be satisfied by X. The inequality constraints must be actual inequalities of the form \(g(X) \ge h(X)\) or \(g(X) \le h(X).\) The equality constraints must be of the form \(g(X) = h(X).\)

rhobeg

Initial value of the internal RHO variable which controls the size of simplex. (Defaults to 1.0)

rhoend

The desired final value rho parameter. It is approximately the accuracy in the variables. (Defaults to 1d-6.)

iprint

Verbose output level. (Defaults to 0)

• 0 - No output
• 1 - Summary at the end of the calculation
• 2 - Each new value of RHO and SIGMA is printed, including the vector of variables, some function information when RHO is reduced.
• 3 - Like 2, but information is printed when F(X) is computed.

maxfun

The maximum number of function evaluations. (Defaults to 1000).

On return, a vector is given:

1. The value of the variables giving the minimum. This is a list of elements of the form var = value for each of the variables listed in X.
2. The minimized function value
3. The number of function evaluations.
4. Return code with the following meanings
   • 0 - No errors.
   • 1 - Limit on maximum number of function evaluations reached.
   • 2 - Rounding errors inhibiting progress.
   • -1 - MAXCV value exceeds RHOEND. This indicates that the constraints were probably not satisfied. User should investigate the value of the constraints.

MAXCV stands for “MAXimum Constraint Violation” and is the value of \(max(0.0, -c1(x), -c2(x),...-cm(x))\) where \(ck(x)\) denotes the k’th constraint function. (Note that maxima allows constraints of the form \(f(x) = g(x)\), which are internally converted to \(f(x)-g(x) >= 0\) and \(g(x)-f(x) >= 0\) which is required by COBYLA).

load("fmin_cobyla") loads this function.

Function: bf_fmin_cobyla
    bf_fmin_cobyla (F, X, Y)
    bf_fmin_cobyla (F, X, Y, optional_args) ¶

This function is identical to fmin_cobyla, except that bigfloat operations are used, and the default value for rhoend is 10^(fpprec/2).

See fmin_cobyla for more information.

load("bf_fmin_cobyla") loads this function.