Linear Optimization: Auxiliary Problem

This lecture covers the formulation of the auxiliary problem in linear optimization, starting with the standard form linear optimization problem and introducing the concept of basic feasible solutions. The instructor explains the process of forming the auxiliary problem, obtaining basic feasible solutions, and computing the reduced costs of original variables. The lecture also delves into the final simplex tableau for the auxiliary problem and the Two-Phase Simplex algorithm. Duality theory is discussed, highlighting the relationship between primal and dual problems, weak duality, and the optimality conditions. The importance of tight lower bounds and the dual problem's role in optimal decision-making are emphasized.