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Efficiently solving SDP relaxation of an integer quadratic program

As a follow up to my comment, where I say that the model has to be interpreted from the primal model side, here it implements the model for $n=1000$ and then tells the modelling layer YALMIP that it ...
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How to ensure the numeric value is always positive in Optimization Python?

Consider a variable transform. Assuming you care about the individual entries of $x$ and not something like its determinant, you can transform the $x_i$ such that the new variable $y_i$ is not bounded ...
Secant Method for finding $\sup f^{-1}(0)$
For reference, the Method of False Position converged accurately and fast for the function $\exp \big(-1000 \cdot (f(x) - 0.001) \big) - 1$