George Mason University
Graduate Course Approval/Inventory Form
Please complete this form and attach a copy of the syllabus for new courses. Forward it as an email
attachment to the Secretary of the Graduate Council. A printed copy of the form with signatures should be
brought to the Graduate Council Meeting. Complete the Coordinator Form on page 2, if changes in this
course will affect other units.
Please indicate: ___X__ NEW
Local Unit: CDS
____ MODIFY
____ DELETE
Graduate Council Approval Date:
Course Designation: CSI
Course Number: 747
Full Course Title: Nonlinear Optimization and Applications
Abbreviated Course Title (24 characters max.): Nonlinear Optimization
Credit hours:
3
Program of Record: CSI Ph.D.
Repeatable for Credit? ___ D=Yes, not within same term
___ T=Yes, within the same term
_N_ N=Cannot be repeated for credit
Up to __ hours
Up to __ hours
Activity Code: __X__ Lecture (LEC) ___ Lab (LAB)
___ Recitation (RCT)
___ Studio (STU)
___ Internship (INT) ___ Independent Study (IND)
___ Seminar (SEM)
Catalog Credit Format: 3:3:0
Course Level: GF(500-600) __ ___ GA(700+) __X__
Maximum Enrollment: 25
For NEW courses, first term to be offered: Spring 2008
Prerequisites: Analytical Geometry and Calculus (MATH 213), Theory of Differential Equations (MATH
216), or permission of instructor.
Catalog Description (35 words or less): Introduction to practical aspects of nonlinear optimization. Covers
applications of optimization algorithms to solving problems in science and engineering. Applications include
data analysis, material science, nanotechnology, mechanics, optical design, shape design and trajectory
optimization.
For MODIFIED or DELETED courses as appropriate:
Last term offered:
Previous Course Abbreviation:
Previous number:
APPROVAL SIGNATURES:
Submitted by:
________Igor Griva _______________ email: __igriva@gmu.edu__
Department/Program:
College Committee:
________________________________ Date: __________________
________________________________ Date: _________________
Graduate Council Representative: ________________________________ Date: __________________
GEORGE MASON UNIVERSITY
Course Coordination Form
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Mathematics Department
Graduate Council approval: ______________________________________________ Date: ____________
Graduate Council representative: __________________________________________ Date: ____________
Provost Office representative: _________________ _______________________
Date: __________
Course Proposal Submitted to the Graduate Council
by
The School of Computational Sciences
1. COURSE NUMBER AND TITLE:
CSI 747 – Nonlinear Optimization and Applications
Prerequisites: Analytical Geometry and Calculus (MATH 213), Theory of Differential Equations (MATH
216), or permission of instructor.
Catalog Description: Introduction to practical aspects of nonlinear optimization. Covers applications of
optimization algorithms to solving problems in science and engineering. Applications include data analysis,
material science, nanotechnology, mechanics, optical design, shape design and trajectory optimization.
2. COURSE JUSTIFICATION:
Course Objectives: After taking this course students should have an understanding of (1) how to apply
optimization algorithms for solving problems arising in the areas of science and engineering including data
analysis, material science, mechanics, optical design, shape design and trajectory optimization, (2) the basic
algorithms used to solve optimization problems, (3) the basics of optimization theory such as optimality
conditions and complexity. This class will provide students with background required for using optimization
in various areas of science and engineering and give an opportunity to begin research in the area of nonlinear
optimization.
Course Necessity: Application of nonlinear optimization to areas of science and engineering is growing
steadily over the past several decades. Today nonlinear optimization is used widely in the areas of navigation,
data analysis, material science, mechanics, power generation and transmission, optical design and trajectory
optimization, to mention a few. This course introduces to the basic concepts of optimization theory and the
algorithms and provides an essential background required for using optimization in various applications. A
particular emphasis is given to the modeling approaches of important problems that can be solved using
optimization techniques, the subject often neglected in other optimization courses.
Course Relationship to Existing Programs: The proposed course provides essential content for students
who plan to earn a degree in the Computational Science and Informatics (CSI) Ph.D program, in any
concentration. Also, the proposed course provides practical knowledge for the students seeking Ph.D. in
Information Technology, Electrical and Computer Engineering, Mathematics and Statistics. This course will
be taught in Spring 2007 under the tentative title “topics in computational sciences” course (CSI749).
Course Relationship to Existing Courses: The proposed course offers new material complementing any
other existing optimization courses at GMU. Unlike OR644 that teaches nonlinear optimization theory and
techniques in detail, the main goal of the proposed course is to teach students how to solve scientific and
engineering problems using optimization algorithms. The proposed course considers problems in the areas of
data analysis, material science, mechanics, optical design, shape design and trajectory optimization and
focuses on practical aspects of nonlinear optimization required for solving these problems. The proposed
course pays special attention to the art of modeling of a scientific or engineering problem as an optimization
problem and emphasizes the importance of certain modeling issues that make the resulting optimization
problem easily solvable by available optimization software. This modeling aspect is not covered in detail in
other optimization courses at GMU.
3. APPROVAL HISTORY:
4. SCHEDULING AND PROPOSED INSTRUCTORS:
Semester of Initial Offering: Spring 2008
Proposed Instructors: Igor Griva, Harbir Lamba, Chi Yang.
5. TENTATIVE SYLLABUS: See attached.
CSI 747
Nonlinear Optimization and Applications
Tentative Syllabus
Prerequisites: Analytical Geometry and Calculus (MATH 213), Theory of Differential Equations (MATH
216), or permission of instructor.
Credits: 3
Date:
Time:
Place:
Instructors:
Contact Info:
Office Hour:
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 techniques in order to solve important problems arising in many areas
of science and engineering. We consider problems in the areas of data analysis, material science,
nanotechnology, mechanics, optical design, shape design and trajectory optimization.
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 a modeling
language AMPL. This language is used as a common mechanism for conveying optimization problems. The
course emphasizes the importance of proper modeling. One of the main points 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. Content:
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Overview of basic concepts of optimization theory: optimality conditions.
Overview of nonlinear optimization algorithms, convergence.
Basic modeling concepts, discretization.
Structural and shape optimization.
Simple linear planning models: production, transportation, diet problems.
Error minimization models: least square model; min variance models: optimal portfolio model.
Data analysis, machine learning, knowledge discovery.
Trajectory optimization and optimal control: Gaddard Rocket, Golf model.
Optimization and material sciences: minimization of potential energy
Optimization and nanotechnology: improving nanodevices.
Optical design and diffraction control: telescope design problems.
Homework and Projects:
There are several projects involving the described applications, which include problem formulation,
modeling and solving using optimization software.
Exams: one midterm and final
Grades:
Homework and projects (40%), Midterm (30%), Final Exam (30%)
Class URL:
http://math.gmu.edu/~igriva/CSI749.html (will be updated)
Note: Presentations in PPT format will be posted online after lectures
Text Book (required):
1. “AMPL: a modeling Language for Mathematical Programming,” Robert Fourer, David M. Gay, and
Brian W. Kernighan, 2002.
Supplement Reference Books:
2. “Practical Methods for Optimal Control using Nonlinear Programming”, J.T. Betts, 2000.
3. “Linear and Nonlinear Programming”, Stephen G. Nash and Ariela Sofer, 1996.
4. “The Nature of statistical learning theory”, V. Vapnik, 1999.