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In mathematics, the spectral radius of a square matrix or a bounded linear operator is the supremum among the absolute values of the elements in its spectrum.

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Optimizing over matrices with spectral radius <1?

Suppose $F(x)$ is a convex objective function on $n\times n$ matrices, and I need to numerically optimize $F$ with the condition that $x$ has spectral radius less than $1$. This might be too hard, so …