A Geometric Approach to Optimal Design Theory
Silvey & Titterington (1973) and Silvey, Titterington & Torsney (1978)
The 1973 paper formulates D- and -equivalence geometrically through Lagrangian duality and gives a convergent monotone D construction. The 1978 paper gives two monotone algorithms on a finite design space. They are direct precedents for sensitivity certificates and monotone determinant updates, but their feasible variables are free design weights at fixed regressors. They do not cover hard partitions whose cell masses and conditional means move together.
- 1973 DOI: https://doi.org/10.1093/biomet/60.1.21
- 1978 DOI: https://doi.org/10.1080/03610927808827719
Biometrika 60(1):21-32. The publisher summary identifies D- and Ds-equivalence as duality theorems proved through Strong Lagrangian Theory on the approximate-design feasible set; this does not transfer strong duality to hard partitions.
Cited by
- Publication-grade audit of the DS19 tilt-DP certificate complexAUDIT-DS-PRACTICAL-CERTIFIED-SOLVER
- Classical Ds optimal-design theoryDS-CLASSICAL-DESIGN-THEORY
- Profiled compile verdict is selected by an observable certificate stateDS-PROFILED-COMPILE-CERTIFICATE
- Scalar-POI tilt-DP gives a valid two-sided certificate with an exact saddle closure gateDS-TILT-DUAL-CERTIFICATE
- The scalar-POI tilt dual can have an order-one strong-duality gapDS-TILT-DUAL-STRONG-DUALITY-FAILS
- Best practical Ds solver with theorem-backed certificateOPEN-DS-PRACTICAL-CERTIFIED-SOLVER
Relevant to
Claims this source bears on without being cited in their proofs.