Course: STAT 31020
Title: Mathematical Computation IIB: Nonlinear Optimization
Instructor(s): Mihai Anitescu
Class Schedule: Sec 01: MW 3:00 PM–4:20 PM in Stuart Hall 101
Textbook(s): Nocedal, Wright, Numerical Optimization, 2nd Edition
Prerequisite(s): STAT 30900/CMSC 37810 or consent of instructor
Description: This course covers the fundamentals of continuous optimization with an emphasis on algorithmic and computational issues. The course starts with the study of optimality conditions and techniques for unconstrained optimization, covering line search and trust region approaches, and addressing both factorization-based and iterative methods for solving the subproblems. The Karush-Kuhn-Tucker conditions for general constrained and nonconvex optimization are then discussed and used to define algorithms for constrained optimization including augmented Lagrangian, interior-point and (if time permits) sequential quadratic programming. Iterative methods for large sparse problems, with an emphasis on projected gradient methods, will be presented. Several substantial programming projects (using MATLAB and aiming at both data-intensive and physical sciences applications) are completed during the course.