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Basic strategy:

an intial grid over the feasible region [l,u] that signifies the degree of resolution desired (this can be refined later, as deemed appropriate) and
an initial baseline design xc in [l,u] at which f is known.

Perform an initial computer experiment:
select N initial design sites,
evaluate the true objective f at the initial design sites, and
construct an initial approximation a of f based on the objective values obtained at the design sites.

Do until a minimizer of f has been confirmed (for the current resolution of the grid) or until the ``budget'' V of evaluations has been exhausted:
find a candidate xt that minimizes a on the grid and treat xt as a site at which a predicts a minimizer for f on the grid.
Evaluate f(xt).
Update the approximation a to include the objective value f(xt).
If f(xt) < f(xc) then let x+ = xt. Else x+ = xc.
Repeat step 3.
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Virginia Torczon