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Extremal Characterizations of the Schur Complement and Resulting Inequalities

Li, Mathias2000

doi:10.1137/S0036144599337290

SIAM Review 42(2):233-246. Theorem 2.2 is the DS11 identity (Loewner-minimal generalized Schur complement with exact attainment set); attributed to M. G. Krein (1947) and Anderson's shorted operator (1971).

Cited by

  • Verification recordPublication-grade audit of the profiled Ds population bridgeAUDIT-DS-POPULATION-BRIDGE
  • Verification recordPublication-grade audit of the DS19 tilt-DP certificate complexAUDIT-DS-PRACTICAL-CERTIFIED-SOLVER
  • CounterexampleThe multivariate-POI matrix-tilt outer ceiling need not be quasiconvexDS-MATRIX-TILT-NONQUASICONVEX
  • Proved here, no precedent foundProfiled compile verdict is selected by an observable certificate stateDS-PROFILED-COMPILE-CERTIFICATE
  • Proved hereVariational form of the profiled objectiveDS-PROFILED-VARIATIONAL
  • Proved here, no precedent foundScalar-POI tilt-DP gives a valid two-sided certificate with an exact saddle closure gateDS-TILT-DUAL-CERTIFICATE
  • CounterexampleThe scalar-POI tilt dual can have an order-one strong-duality gapDS-TILT-DUAL-STRONG-DUALITY-FAILS
  • Proved here, no precedent foundBest practical Ds solver with theorem-backed certificateOPEN-DS-PRACTICAL-CERTIFIED-SOLVER
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