Reference · The Applied Higher-Order Functions catalogue

rainbow.algorithms.proofs.ahof.backtracking

The Applied Higher-Order Functions cataloguesrc/rainbow/algorithms/proofs/ahof/backtracking.clj1 definitions, 4 theorems

AHoF O14 Backtracking Line Search: shrink the step until the Armijo sufficient- decrease condition holds -- the new objective is at or below the predicted decrease bound f(x) + c*alpha*slope: sufficient-decrease? new-value armijo-bound = decide (new-value <= armijo-bound). Proved native and axiom-free (decision, two positive instances, at-most certificate, negative instance). 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 4 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.backtracking` prints this classification.

backtrack/sufficient-decrease? :
  (x₁ x₂ : ℚ≥0)
  → data/Bool

backtrack/accepts-sufficient-decrease :
  → search/poll-improves 1/2 3/4 = data/true

backtrack/boundary-accepts :
  → search/poll-improves 1/2 1/2 = data/true

backtrack/armijo-certificate :
  → 1/2 ≤ 3/4

backtrack/rejects-insufficient :
  → search/poll-improves 3/4 1/2 = data/false