BOBYQA solves bound constrained optimization problems without using derivatives of the objective function, which makes it a derivative-free algorithm. The algorithm solves the problem using a trust region method that forms quadratic models by interpolation. One new point is computed on each iteration, usually by solving a trust region subproblem subject to the bound constraints, or alternatively, by choosing a point to replace an interpolation point so as to promote good linear independence in the interpolation conditions.
In the comment of the software's source code, it is said that the name BOBYQA denotes "Bound Approximation BY Quadratic Approximation", which seems to be a typo of "Bound Optimization BY Quadratic Approximation".
- Powell, M. J. D. (June 2009). The BOBYQA algorithm for bound constrained optimization without derivatives (PDF) (Report). Department of Applied Mathematics and Theoretical Physics, Cambridge University. DAMTP 2009/NA06. Retrieved 2014-02-14.
- Powell, M. J. D. (2004). "Least Frobenius norm updating of quadratic models that satisfy interpolation conditions". Mathematical Programming. Springer. 100: 183–215. doi:10.1007/s10107-003-0490-7.
- "A repository of Professor M. J. D. Powell's software". Retrieved 2014-01-18.
- "Source code of BOBYQA software". Retrieved 2014-02-14.