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1 parent 00ff79c commit 0e74bb6Copy full SHA for 0e74bb6
botorch/test_functions/synthetic.py
@@ -586,6 +586,19 @@ def evaluate_true(self, X: Tensor) -> Tensor:
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class Powell(SyntheticTestFunction):
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+ r"""Powell synthetic test function.
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+
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+ `d`-dim function (usually evaluated on hypercube `[-4, 5]^d`):
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+ P(x) = sum_{i=1}^d/4 (
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+ (x_{4i-3} + 10 x_{4i-2})**2
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+ + 5 (x_{4i-1} - x_{4i})**2
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+ + (x_{4i-2} - 2 x_{4i-1})**4
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+ + 10 (x_{4i-3} - x_{4i})**4
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+ )
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+ P has a global minimizer at `z = (0, ..., 0)` with `P(z) = 0`.
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+ """
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_optimal_value = 0.0
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