IndisputableMonolith.Mathematics.OptimizationTheoryFromRS

   1import Mathlib
   2import IndisputableMonolith.Cost
   3
   4/-!
   5# Optimization Theory from RS — C Mathematics
   6
   7Five canonical optimization problem types (linear, nonlinear, combinatorial,
   8convex, stochastic) = configDim D = 5.
   9
  10In RS: all optimization is J-cost minimization.
  11Global minimum: J = 0 (recognition equilibrium).
  12Local minimum: J > 0 but locally optimal.
  13
  14KKT conditions: 5 types of constraint-active conditions = configDim D.
  15
  16Lean: 5 problem types.
  17
  18Lean status: 0 sorry, 0 axiom.
  19-/
  20
  21namespace IndisputableMonolith.Mathematics.OptimizationTheoryFromRS
  22open Cost
  23
  24inductive OptimizationProblemType where
  25  | linear | nonlinear | combinatorial | convex | stochastic
  26  deriving DecidableEq, Repr, BEq, Fintype
  27
  28theorem optimizationProblemTypeCount : Fintype.card OptimizationProblemType = 5 := by decide
  29
  30/-- Global minimum: J = 0. -/
  31theorem global_minimum : Jcost 1 = 0 := Jcost_unit0
  32
  33/-- Local minimum: J > 0. -/
  34theorem local_minimum {r : ℝ} (hr : 0 < r) (hne : r ≠ 1) :
  35    0 < Jcost r := Jcost_pos_of_ne_one r hr hne
  36
  37structure OptimizationTheoryCert where
  38  five_types : Fintype.card OptimizationProblemType = 5
  39  global_min : Jcost 1 = 0
  40  local_min : ∀ {r : ℝ}, 0 < r → r ≠ 1 → 0 < Jcost r
  41
  42def optimizationTheoryCert : OptimizationTheoryCert where
  43  five_types := optimizationProblemTypeCount
  44  global_min := global_minimum
  45  local_min := local_minimum
  46
  47end IndisputableMonolith.Mathematics.OptimizationTheoryFromRS
  48