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cobyla

performs nonlinear constrained optimization without derivatives

Calling Sequence

[x_opt, eval_func] = cobyla(x0, func, nb_constr, rhobeg, rhoend, message, eval_func_max)

Parameters

Input parameters

x0

the starting point

func

the function to minimize. This function must have the following prototype:

[fval, conval, info] = fobj(x)

where:

  • fval is the value of the objective function.

  • conval is the value of the constraints.

  • info is a return status:

    • 0 - no error occurs

    • 1 - a problem occurs.

nb_constr

number of constraints.

rhobeg

a reasonable initial change to the variables.

rhoend

the required accuracy for the variables.

message

verbosity level. Allowed values are:

  • 0 (COBYLA_MSG_NONE) - no messages

  • 1 (COBYLA_MSG_EXIT) - exit reasons

  • 2 (COBYLA_MSG_ITER) - rho and sigma changes

  • 3 (COBYLA_MSG_INFO) - Informational messages

eval_func_max

the maximum number of function evaluations

Output parameters

x_opt

the solution found by cobyla.

eval_func

the number of function evaluations done.

status

the return code of cobyla.

  • -2 (COBYLA_EINVAL) - N<0 or M<0.

  • -1 (COBYLA_ENOMEM) - Memory allocation failed.

  • 0 (COBYLA_NORMAL) - Normal return from cobyla.

  • 1 (COBYLA_MAXFUN) - Maximum number of function evaluations reach.

  • 2 (COBYLA_ROUNDING) - Rounding errors are becoming damaging.

  • 3 (COBYLA_USERABORT) - User requested end of minimization.

Description

This software is a Scilab interface of COBYLA2, a contrained optimization by linear approximation package developed by Michael J. D. Powell in Fortran.

The original source code can be found at: http://plato.la.asu.edu/topics/problems/nlores.html

Examples

nb_constr_test_1 = 0;
xopt_test_1 = [-1 0]';

function [f, con, info]=test_1(x)
  d__1 = x(1) + 1.;
  d__2 = x(2);
  f = d__1 * d__1 * 10. + d__2 * d__2;
  con = 0;
  info = 0;
endfunction

rhobeg = 1;
rhoend = 1e-3;
message_in = 3;
eval_func_max = 200;

x0 = ones(xopt_test_1);
[x_opt, status, eval_func] = cobyla(x0, test_1, nb_constr_test_1, rhobeg, rhoend, message_in, eval_func_max);

disp(x_opt);
disp(xopt_test_1);

Authors

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