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Strict positivity, $x > 0$, is equivalent to the existence of nonnegative variable, $r \geq 0$, such that $xr \geq 1$. This means that it can be represented in second-order cone programming by the conic quadratic constraint $$x+r \geq \sqrt{ (x-r)^2 + 1^2 }.$$ To see this, just square both sides of the inequality and expand. Conclusively, MISOCP (mixed-...

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