2 problems

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Shapiro's conjecture on the upper bound for the structured Rayleigh quotient
Let $H \in \operatorname{Herm}(n)$ and $S_0,\ldots,S_m \in \operatorname{Sym}(n)$ , and let $m_{h S_0 \ldots S_m}$ denote the quantity optimized in the paper. An upper bound for thi…
Conjectureopennumerical-optimization rayleigh-quotients structured-eigenvalue-problemsarXiv posted 3 days ago
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Miclo's disjoint low-Rayleigh-quotient family conjecture
Miclo's conjecture. It should be possible to find a family $\{\psi_i\}$ of $k$ pairwise disjointly supported functions $\psi_i:V\to\ell_2$ such that each $\mathcal R_G(\psi_i)$ is…
Conjectureopengraph-partitioning rayleigh-quotients spectral-graph-theoryarXiv posted 3 days ago

Shapiro's conjecture on the upper bound for the structured Rayleigh quotient