Linear Programming Notes
A consolidated set of notes on linear programming, including standard forms, feasible regions, duality, complementary slackness, Farkas' lemma, and the geometric logic of the simplex method.
Academic Notes · Optimization · Linear Methods
Linear Programming
Notes on linear optimization, feasible regions, polyhedra, primal-dual formulations, weak and strong duality, complementary slackness, Farkas' lemma, simplex geometry, and sensitivity analysis.
Linear Programming
Notes and drafts.
This section collects notes on the geometry, algebra, and duality theory of linear programming. The focus is on polyhedral feasible regions, primal-dual structure, certificates of optimality and infeasibility, and algorithmic interpretation.
Linear Programming Duality
A focused note on primal-dual linear programs, weak duality, strong duality, complementary slackness, and economic interpretations of dual variables.
Farkas' Lemma and Theorems of Alternatives
Notes on alternative systems, infeasibility certificates, separating hyperplanes, and how Farkas' lemma supports linear programming duality.
Simplex Method: Geometry Before Algorithm
A geometric introduction to vertices, bases, basic feasible solutions, adjacent extreme points, pivoting, and objective improvement.
Sensitivity Analysis
Notes on shadow prices, reduced costs, right-hand-side perturbations, objective coefficient changes, and stability of optimal bases.