Reference · The Applied Higher-Order Functions catalogue

rainbow.algorithms.proofs.ahof.epsilon-constraint

The Applied Higher-Order Functions cataloguesrc/rainbow/algorithms/proofs/ahof/epsilon_constraint.clj1 definitions, 3 theorems

AHoF O67 Epsilon-Constraint Method (multi-objective): optimize one objective while the others are turned into inequality constraints f_i <= epsilon_i. A candidate is feasible for the constrained objective exactly when its value is within the epsilon bound: feasible? value epsilon = decide (value <= epsilon) over exact rationals. Proved native and axiom-free: the feasibility decision; that a value within the bound is feasible; the certificate that a feasible value really is at most epsilon (native nnrat/at-most); and that a value exceeding the bound is infeasible. Requires audit/decide-nnrat-at-most, nnrat/at-most, nnrat/decide-at-most-true-sound (all 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.epsilon-constraint` prints this classification.

epsilon-constraint/feasible? :
  (x₁ x₂ : ℚ≥0)
  → data/Bool

epsilon-constraint/within-bound-feasible :
  → ce-is/elite? 1/2 3/4 = data/true

epsilon-constraint/feasible-within-epsilon :
  → 1/2 ≤ 3/4

epsilon-constraint/over-bound-infeasible :
  → ce-is/elite? 3/4 1/2 = data/false