i know we can write a \geq \frac{1}{b} as [a +b, a - b, 2] in SecondOrderCone() or a + b \geq ||(a-b, 2)||_2
But how can i rewrite a \leq \frac{1}{b} with Second Order cones, power cones, exponential cones, basically anything that mosek offers?
You can’t because this is a non-convex constraint. Mosek is a convex optimization solver.
oh i see, thanks!
is there any nice of modeling t\geq (\log x)^2 when x\geq 1?
If you want to use Mosek, you need convex constraints: Convex function - Wikipedia.
This is not convex.
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If x only appears through \log(x), e.g., there are no other constraints of the form x + y \leq 1, then you can write z = \log(x) \geq 0 and replace all occurrences of \log(x) by z \geq 0.
Here, t \geq (\log x)^2 becomes t \geq z^{2}, which is convex in the t, z space.
Solve the resulting problem w.r.t z, and recover x = \exp(z) \geq 1.
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