IE 534: Nonlinear Programming

Course Description

Optimization problems involve choosing from a selection of feasible solutions, a solution that is a best choice, according to some merit function. For example, the best way to ship 100,000 gizmos from Seattle to New York. In this context, "feasible" refers to the options available and "best" could refer to least cost, safest, fastest, or some combination of measures. More generally, "feasible" is usually described by a set of constraint function and "best" by an optimization function. Such problems are faced by engineers, economists, scientists, planners, managers, and operations researchers.

IE 534 covers theoretical and computational methods to solve such problems when at least one constraint or optimization function is not linear. Topics include convexity, optimality conditions, Newton’s method, Lagrange multipliers, search algorithms for unconstrained and constrained problems, as well as barrier and penalty methods. Students taking this course will be able to answer such questions as:

• What sort of problems can I solve with these theories and techniques?
• How can I frame a problem to improve my chances of success?
• How would I know if a given solution is optimal?
• What pitfalls are there in this sort of analysis and how can I avoid them?
• What are the tradeoffs among the different possible methods?
• Why do I have to bother with this theory?
• Why can't I trust every answer my computer gives me?
• How can I solve really big problems?

In addition, students will employ MatLab and LINGO. MatLab is a general-purpose application that will make it easier to see what the algorithms are doing. LINGO is a representative optimization package which can be used to solve very large problems.

Intended Students: Masters-level students who want to gain a practical understanding of modeling and solving nonlinear optimization problems that is firmly supported by theory.

Expected Background: The student should have completed differential and integral calculus. A knowledge of vector mathematics is helpful, but not required. A background in linear programming beyond the undergraduate level may also be helpful, but also not required.

Details:

 Instructor: John Mullen, Tel:(505)646-2958, email: jomullen@nmsu.edu Texts: Nonlinear Programming: Theory and Algorithms, 3rd ed., by Bazaraa, Sherali, and Shetty. 2006. ISBN: 0-471-48600-0 Computer: Web-CT Site: https://salsa.nmsu.edu/ MatLab LINGO

Revision Date: January 5, 2007 by jpm.