Nonlinear Programming

Course Description

The course will introduce the fundamentals of nonlinear optimization, geared towards doctoral and advanced graduate students. The emphasis is on the theoretical foundations of optimization, classical mathematical programming, as well as models and solution techniques. Although some applications and algorithms are discussed, the emphasis is theoretical. The focus of the course will be on convex analysis (convex sets, separation theorems, convex functions), optimality conditions (Fritz-John & Karush-Kuhn-Tucker), Lagrangian duality, and iterative solution methods. This course is primarily intended for doctoral students; nonetheless, as a technical elective, it may be suitable for advanced master’s students with an appropriate background in operations research. At the end of the course, students will be able to (1) mathematically prove fundamental results in optimization, (2) recognize and formulate nonlinear optimization problems, (3) identify when a problem is convex, (4) understand classical results characterizing optimal solutions to these problems, (5) use these classical results in application problems and design of algorithms, and (6) use optimization software (e.g., Pyomo) to implement optimization models.

Code

IE 671

Credits

3

Subject

Industrial and Systems Engineering

Programs That Include This Course

• Doctoral Doctor of Philosophy in Computational and Data Enabled Sciences
• Doctoral Doctor of Philosophy in Materials Design and Innovation
• Master's Master of Engineering in Engineering Management
• Master's Master of Science in Materials Design and Innovation