Deterministic Optimization Models in OR
This course introduces students to deterministic optimization models in operations research. Students learn to formulate, analyze, and solve mathematical optimization models that represent real-world problems. Only deterministic models are considered, i.e., no uncertainty in the models is allowed. The first part of the course covers linear programming and the simplex algorithm, as well as related topics. The second part of the course discusses other types of optimization models, including transportation, network, and integer problems. If time permits, nonlinear models are briefly discussed.
The goal of this course is to introduce the basic theoretical principles underlying nonlinear optimization and the numerical algorithms that are available to solve them. We begin with fundamental (sub)gradient methods and Newton’s method for unconstrained optimization, which represent the core of numerous nonlinear optimization algorithms. We then develop an understanding of optimality conditions and duality in the presence of nonlinear functions, ending by discussing modern numerical methods for nonlinear constrained optimization, and their associated convergence properties.