Convex Analysis

IE 515 builds the geometric and analytic machinery behind convex optimization — separation theorems, subgradients, conjugate functions, and duality — so that you stop treating optimality conditions as recipes and start seeing why they hold. The work is proof-heavy: weekly homework sets and a written final where you derive results rather than plug into solvers, working through Rockafellar and van Tiel. It's the theoretical backbone for graduate work in optimization, OR, and machine learning, and it's where Lagrangians, KKT, and dual programs stop being black boxes and become consequences of a few clean ideas about convexity.