Spring 2007

CSI 749 / MATH 689 Nonlinear optimization and Applications

Schedule: W 7:20-10:00 pm, East Building 134 Instructor: Igor Griva, igriva@gmu.edu , (703) 993-4511 Office hours: MW 3:30 - 4:30 pm, Research 1 Rm 344 Prerequisite: Permission of instrustor Webpage: math.gmu.edu/~igriva/CSI749.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: March 24 (points 0 - 100) Final Exam : May 9 (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, nanotechnology, material science, 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. In order to take this class students have to be familiar with basic concepts of programming, optimization and ordinary differential equations. Knowledge of linear and nonlinear programming is recommended.