CLRS-Lean
Chapter 29. Linear Programming
29.5. The Initial Basic Feasible Solution

Imports

import CLRSLean.Chapter_29.Section_29_5_The_Initial_Basic_Feasible_Solution.ArtificialLP
import CLRSLean.Chapter_29.Section_29_5_The_Initial_Basic_Feasible_Solution.InitialPivot
import CLRSLean.Chapter_29.Section_29_5_The_Initial_Basic_Feasible_Solution.PhaseOne
import CLRSLean.Chapter_29.Section_29_5_The_Initial_Basic_Feasible_Solution.LockVariable
import CLRSLean.Chapter_29.Section_29_5_The_Initial_Basic_Feasible_Solution.RestoreObjective
import CLRSLean.Chapter_29.Section_29_5_The_Initial_Basic_Feasible_Solution.PhaseTwoStart
import CLRSLean.Chapter_29.Section_29_5_The_Initial_Basic_Feasible_Solution.PhaseTwoBridge
import CLRSLean.Chapter_29.Section_29_5_The_Initial_Basic_Feasible_Solution.InitializedSimplex
import CLRSLean.Chapter_29.Section_29_5_The_Initial_Basic_Feasible_Solution.DualProjection
import CLRSLean.Chapter_29.Section_29_5_The_Initial_Basic_Feasible_Solution.GeneralStrongDuality

29.5 The initial basic feasible solution

This section formalizes the textbook phase-I auxiliary program and the initialized SIMPLEX procedure. The textbook deletes the artificial variable before phase II; the fixed-dimension dictionary model instead adds the equivalent lock x₀ ≤ 0. Together with auxiliary nonnegativity this forces x₀ = 0, preserves exactly the original feasible assignments, and avoids a dimension-changing tableau operation.

Implementation details

              namespace CLRSnamespace Chapter29end Chapter29end CLRS