Reference · Signed rationals

rainbow.math.rational.signed.lp-capacity-sensitivity

Signed rationalssrc/rainbow/math/rational/signed/lp_capacity_sensitivity.clj0 definitions, 2 theorems

Capacity sensitivity for signed LP dual bounds. Moving capacities from b to b' changes the dual bound by at most the sum of exact distances between corresponding weighted capacity terms. This form is valid for signed prices. It is a checked output-bound theorem, not a claim about an LP executable or its numerical implementation.

Depends onmath.linear.vector.dot-distance-boundmath.linear.vector.dot-commutative

optimization/signed-lp-capacity-bound-distance :
  (prices capacities changed-capacities : List ℚ)
  (capacity-shape : vector/same-shape capacities changed-capacities)
  → signed/distance (vector/dot capacities prices) (vector/dot changed-capacities prices) ≤ vector/dot-distance-sum prices capacities changed-capacities

optimization/signed-lp-capacity-bound-distance-bounded :
  (prices capacities changed-capacities : List ℚ) (upper : ℚ)
  (capacity-shape : vector/same-shape capacities changed-capacities)
  (budget-bound : vector/dot-distance-sum prices capacities changed-capacities ≤ upper)
  → signed/distance (vector/dot capacities prices) (vector/dot changed-capacities prices) ≤ upper