The BOBYQA Solver
The name BOBYQA is an acronym for bound optimization by quadratic approximation. The basic idea of the method is to iteratively approximate the objective function by a quadratic model which is valid in a region around the current iterate, the so-called trust region. The quadratic model is updated by minimizing the Frobenius norm of the difference in the Hessians of the two consecutive quadratic approximations. The implementation in COMSOL is based on Ref. 3. There are, however, some modifications:
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The number of interpolation conditions is fixed to 2n+1 where n is the number of control variables, since the updating of the quadratic approximation requires only O(n2) operations in that case.
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Since the COMSOL implementation works in scaled control variables, the initial trust region radius is fixed at 0.2 in relative terms.
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The RESCUE subroutine is not included due to the unavailability of test problems that would invoke that procedure. Instead, an error message is given.