Math 464 [CAPS] – Linear
Linear optimization (or linear programming, LP) is the fundamental branch of optimization, with applications to many areas including life sciences, computer science, defense, finance, telecommunications, transportation, etc. Other types of optimization typically use LP as the underlying model. This course will provide an integrated view of the theory, solution techniques, and applications of linear optimization. There will be a fair bit of emphasis on theorems and their proofs. The treatment of most topics will begin with a geometric point of view, followed by the development of the solution techniques (algorithms), which are described using linear algebra. A background in linear algebra and multivariate calculus is assumed. Topics covered include linear programming formulations, geometry of linear programming, the simplex method, duality, sensitivity analysis, interior point methods, and integer programming basics. Apart from problems involving proofs, the student will use Octave (or Matlab) or another programming language (e.g., Python) for implementing some of the computations and algorithms. A state-of-the-art modeling software such as AMPL will also be introduced for solving problems modeling real life situations.