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Given a modest number of evaluations of the objective (a ``budget'') produce

a better ``picture'' of the behavior of the objective in the region(s) of interest and
do so in a way that is guaranteed--in theory--to converge to at least a local stationary point of the function.
With a limited number of objective evaluations, it may not be possible to ensure convergence to a stationary point, but satisfying the conditions required by the theory provides some assurance that this is a sensible approach to the design optimization problem.

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Virginia Torczon