Linear Programming: Simplex Method and Duality

Linear programming is a foundational discipline behind modern optimization, logistics, and data science. This written course provides a step-by-step introduction to the mathematical principles and practical algorithms used to formulate and solve linear optimization problems. You will begin with foundational definitions, convex geometry, and standard form representations before examining algorithmic problem-solving techniques and duality theory in depth. What you'll learn: - Understand standard form representations and geometric foundations of linear programs - Apply the simplex method to compute basic feasible solutions systematically - Master pivoting rules and techniques to handle degeneracy and avoid cycling - Analyze polytope geometry, edge paths, and theoretical step bounds - Formulate dual linear programs and interpret shadow prices accurately - Prove and apply weak duality, strong duality, and Farkas' lemma - Explore modern computational modeling workflows for optimization problems The text begins with key terminology and geometric intuition before guiding you through step-by-step algebraic iterations, edge-case handling, and theoretical duality proofs with practical written exercises. Designed for beginners and analytical thinkers, no advanced background in optimization is required. Start reading to build a solid foundation in linear optimization algorithms today.