Result · E-BB-APPLIES

Refinement bounds also apply to E

Proved herepublication: internal

Meaning

Information monotonicity under refinement supplies a branch-and-bound upper bound for the smallest-eigenvalue criterion.

Statement

lambda_min is Loewner-monotone, so refinement information provides valid upper bounds for E branch-and-bound.

Relationships

Rests on

Refinement upper bounds for Loewner-monotone criteriaGENERAL-REFINEMENT-BB

The full chain beneath it

Refinement monotonicityFI-REFINEMENT-MONOTONICITYdepth 2
Quantized Fisher-information identityFI-QUANT-IDENTITYdepth 3

Open next door

Characterize criteria with finite exchange => first-order geometryOPEN-CRITERION-CHARACTERIZATION
Quantitative E necessity bound under spectral gapOPEN-E-SPECTRAL-GAP-BOUND

Local graph

Prerequisites to the left, what it enables or raises to the right, boundary cases below. Open in the map.

Proof

E5. Safe E screening and B&B

G2 gives a sound rejection rule. Exact post-move $\lambda_{\min}$ evaluation can be reserved for screened-in candidates. Refinement B&B applies because $\lambda_{\min}$ is Loewner-monotone.

From E-optimality · chapter contents