$$\begin{array}{ll} \text{maximize} & t\\ \text{subject to} & \mathbf{A} -t \mathbf{B} \succeq 0\end{array}$$
where $\mathbf{A}\succeq0$ and $\mathbf{B}\succeq0$. I want to ask one question. Can I get $t$ in closed form?
2026-02-22 21:18:41.1771795121
Can I get a closed form solution of this SDP?
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This is the smallest generalized eigenvalue of the pair $(A,B)$. In MATLAB, you would compute it as
min(eig(A,B))