Fall 2016

CSI 747 / MATH 689 Nonlinear optimization and Applications

Schedule: W 7:20-10:00 pm, Exploratory Hall 4106 Instructor: Igor Griva, igriva@gmu.edu , (703) 993-4511 Office hours: W 10:00 - 11:00 pm, Exploratory Hall, Rm 4114 Prerequisite: Permission of instrustor Webpage: math.gmu.edu/~igriva/CSI747.html Text: Robert Fourer, David M. Gay, and Brian W. Kernighan, AMPL: A Modeling Language for Mathematical Programming. Duxbury Press / Brooks/Cole Publishing Company, 2002 Exams: There is one midterm exam: October 29 (points 0 - 100) Final Exam : December 14 (points 0 - 100) Final score: F = 0.3*(Midterm) + 0.4*(Homework / Projects) + 0.3*(Final Exam) General description: The course focuses on practical aspects of nonlinear optimization. The main goal of this class is to show students how to use modern optimization tools in order to solve important problems arising in many areas of science and engineering. We consider problems in the following areas: data analysis, computational learning, mechanics, optical design, trajectory optimization, shape optimization, optimal control and finance. The course demonstrates that many real world problems can be modeled as optimization problems and solved by widely available optimization tools. Throughout the course we present various optimization models and demonstrate how to solve them using optimization software. These models are expressed in the AMPL modeling language. This language is used as a common mechanism for conveying optimization problems. The course emphasizes the importance of proper modeling. One of the main point this course illustrates is that often a real world problem can have multiple equivalent mathematical formulations some of which are numerically tractable while others are not. Basics of nonlinear optimization theory will be also discussed. Additional text on optimization methods: Igor Griva, Stephen G. Nash, Ariela Sofer, Linear and Nonlinear Optimization, Second Edition, SIAM, Philadelphia, 2009 Instructions how to install and AMPL with solvers