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### 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.

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