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BOBYQA (Bound Optimization BY Quadratic Approximation) is a free numerical optimization solver released in 2009 for derivative-free optimization of nonlinear problems (NLP) with at most box constraints lb_i <= x_i <= ub_i.

Also this solver is used in OpenOpt Factor Analysis tool for experiment planning.

Here is original advertisement of its author Michael J.D. Powell:

This Fortran software seeks the least value of a function of several variables without requiring any derivatives of the objective function. It was developed from my NEWUOA package for this calculation in the unconstrained case. The main new feature of BOBYQA, however, is that it allows lower and upper bounds on each variable. The name BOBYQA denotes Bound Optimization BY Quadratic Approximation.

Please send an e-mail to me at if you would like to receive a free copy of the Fortran software. As far as I know BOBYQA is the most powerful package available at present for minimizing functions of hundreds of variables without derivatives subject to simple bound constraints. There are no restrictions on its use. I would be delighted if it becomes valuable to much research and many applications.

January 7th, 2009 Michael J.D. Powell.

To use BOBYQA from OpenOpt you should have nlopt with it Python API installed.

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