Reference · The Applied Higher-Order Functions catalogue

rainbow.algorithms.proofs.ahof.dcp

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

AHoF O57 Disciplined Convex Programming: express a convex program from a grammar of convex atoms so feasibility of each convex inequality constraint g(x) <= b reduces to a decidable exact-rational comparison of the constraint value against its bound: constraint-satisfied? value bound = decide (value <= 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.dcp` prints this classification.

dcp/constraint-satisfied? :
  (x₁ x₂ : ℚ≥0)
  → data/Bool

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

dcp/tight-constraint :
  → ce-is/elite? 1/2 1/2 = data/true

dcp/feasibility-certificate :
  → 1/2 ≤ 3/4

dcp/infeasible-point :
  → ce-is/elite? 3/4 1/2 = data/false