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odow authored Nov 7, 2023
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For each nonlinear term, EAGO makes use of factorable representations to
construct bounds and relaxations. In the case of $f(x) = x (x - 5) \sin(x)$, a
list is generated and rules for constructing McCormick relaxations are used to
formulate relaxations in the original decision space, $X$ [[1](#references)]:
formulate relaxations in the original decision space, $X$ [1]:

- $v_{1} = x$
- $v_{2} = v_{1} - 5$
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<img src="https://github.com/PSORLab/EAGO.jl/blob/master/docs/src/mccormick/Figure_1.png" width="60%" height="60%"/>
</p>

Either these original relaxations, differentiable McCormick relaxations
[[2](#references)], or affine relaxations thereof can be used to construct
relaxations of optimization problems useful in branch and bound routines for
global optimization. Utilities are included to combine these with algorithms for
relaxing implicit functions [[3](#references)] and forward-reverse propagation
of McCormick arithmetic [[4](#references)].
Either these original relaxations, differentiable McCormick relaxations [2], or
affine relaxations thereof can be used to construct relaxations of optimization
problems useful in branch and bound routines for global optimization. Utilities
are included to combine these with algorithms for relaxing implicit functions
[3] and forward-reverse propagation of McCormick arithmetic [4].

## License

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## Use with JuMP

EAGO makes use of JuMP to improve the user's experience in setting up
optimization models. Consider the "process" problem instance from
[[5](#references)]:
optimization models. Consider the "process" problem instance from [5]:

$$
\begin{align*}
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