Linear Programming

Linear programming is the workhorse of operations research, and this graduate course builds it from the ground up: how to take a messy real-world decision problem, cast it as the optimization of a linear objective over linear constraints, and then actually solve it. You'll spend the semester translating problems into LP form, dissecting the simplex method through its geometry and algebra, and working through duality, sensitivity analysis, and modern extensions like interior point methods and semidefinite programming via Bertsimas and Tsitsiklis, with regular homework that's heavy on formulation and proof. Expect this to be the foundation for almost everything that follows in optimization, from integer and network programming to stochastic and conic models.