Reference · The Applied Higher-Order Functions catalogue

rainbow.algorithms.proofs.ahof.cutting-planes

The Applied Higher-Order Functions cataloguesrc/rainbow/algorithms/proofs/ahof/cutting_planes.clj2 definitions, 3 theorems

AHoF O73 Cutting Planes: solve an integer/convex program by iteratively adding linear inequalities (cuts) that remove the current fractional/infeasible LP solution while preserving all true solutions. The current point is feasible for a constraint a.x <= b when its left-hand side stays within the bound; a cut is added exactly when it does not: feasible? lhs bound = decide (lhs <= bound) add-cut? lhs bound = NOT (feasible? lhs bound) (boolean negation via if-data) over exact rationals. Proved native and axiom-free: the feasibility decision, the add-cut complement, a satisfied point (no cut) and a violated point (cut added). Requires audit/decide-nnrat-at-most, logic/if-data (both in the D63 checkpoint). Scope (measured by the kernel): this module has 3 worked instances (statements about specific values). None of its theorems is a guarantee about the algorithm for all inputs; `lein verify rainbow.algorithms.proofs.ahof.cutting-planes` prints this classification.

cutting-planes/feasible? :
  (x₁ x₂ : ℚ≥0)
  → data/Bool

cutting-planes/add-cut? :
  (x₁ x₂ : ℚ≥0)
  → data/Bool

cutting-planes/satisfied-no-cut :
  → cutting-planes/add-cut? 1/2 3/4 = data/false

cutting-planes/point-feasible :
  → ce-is/elite? 1/2 3/4 = data/true

cutting-planes/violated-cut-added :
  → cutting-planes/add-cut? 3/4 1/2 = data/true