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Linear Matrix Inequalities (LMIs)

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Inverting a linear system of inequalities

Suppose I have a set of inequalities $l \leq Ax \leq r$ for vectors $l,r$ and matrix $A$. I am trying to bound $x$ using a function of $l,r: f(l) \leq x \leq g(r)$ for some $f,g$. When can we invert t …
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