Optimization: Primal and Dual
A two-part lesson from constrained minimization to Lagrangian duality.
This lesson develops one small optimization problem carefully enough that every geometric and algebraic step can be seen.
1. A Simple Optimization Problem
State a constrained minimization problem, identify its feasible set, solve it analytically, and verify the answer numerically and graphically.
Prerequisites: algebra, derivatives, NumPy, and Matplotlib.
2. Primal and Dual Problems
Construct the Lagrangian, derive the dual function, compare primal and dual bounds, and verify strong duality through the KKT conditions.
Prerequisites: 1. A Simple Optimization Problem.