Syllabus - IE 417: Advanced Mathematical Programming...

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IE 417: Advanced Mathematical Programming Instructor: Dr. Ted Ralphs Office: 473 Mohler Lab Phone: 8-4784 E-mail: tkralphs@lehigh.edu Office Hours: M 10:00-11:00, TR 2:30-3:30 Web page: http://www.lehigh.edu/~tkr2 Course web page: http://www.lehigh.edu/~tkr2/teaching/ie417/ Course meeting time: TR 4:10-5:25 453 Mohler Lab Description of Course This course will address a number of advanced topics in mathematical programming with particular emphasis on optimization problems with non-linear objective function and/or non-linear constraints. Topics will include convex analysis, unconstrained and constrained optimization, non-linear duality theory, Lagrangian relaxation, and algorithmic methods for solving non-linear programs. The algorithmic methods covered will include descent methods, Newton's method, conjugate gradient methods, and penalty and barrier methods. If time permits, we will also consider interior point methods for linear programming. Course Objectives The goal of this course is for students to 1. Continue to improve their ability to rigorously prove mathematical statements. 2. Cultivate an ability to perform accurate self-assessment of their work. 3. Review and extend knowledge and understanding of the underlying mathematical foundations of the field of optimization. 4. Develop an understanding of optimality conditions for both constrained and unconstrained nonlinear optimization problems. 5. Learn how and when to apply optimality conditions for practical problem solving. 6. Learn and apply algorithmic and computational techniques for solving mathematical programs, particularly non-linear. 7. Understand the computational issues involved in solving non-linear programs. Required Text Mokhtar S. Bazaraa, Hanif D. Sherali, and C.M. Shetty, Nonlinear Programming: Theory and Algorithms, Wiley (1993). Suggested Supplementary Materials Daniel Solow, How to Read and Do Proofs: An Introduction to Mathematical Thought Processes, Wiley (2001).
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Daniel J. Velleman, How to Prove It: A Structured Approach, Cambridge University Press (1994). Course Requirements 1. Lectures :: Students will be expected to attend and participate in the lectures. Part of the grade will be determined by overall class participation. Lecture materials, most likely in the form of Power Point slides, will be available for reference before the lecture on the course web page. 2. Reading
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This note was uploaded on 02/29/2008 for the course IE 417 taught by Professor Linderoth during the Spring '08 term at Lehigh University .

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Syllabus - IE 417: Advanced Mathematical Programming...

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