This resource covers: The Practical Importance of Duality; Review of Convexity; A Separating Hyperplane Theorem; Definition of the Dual Problem; Steps in the Construction of the Dual Problem; Examples of Dual Constructions; The Dual is a Concave Maximization Problem; Weak Duality; The Column Geometry of the Primal and Dual Problems; Strong Duality; Duality Strategies; Illustration of Lagrange Duality in Discrete Optimization.