COURSE SYLLABUS
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COURSE NUMBER: ECE 6397-04, Fall 2012
NAME OF COURSE: Selective Topics on Optimization
NAME OF INSTRUCTOR: Zhu Han, W302, 713-743-4437(o), 301-996-2011(c)
http://www2.egr.uh.edu/~zhan2/ http://wireless.egr.uh.edu/
Office Hours: M 10am-2:00 pm or by appointment
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The information contained in this class syllabus is subject to change without
notice. Students are expected to be aware of any additional course policies
presented by the instructor during the course.
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Learning Objectives
This class considers various optimization techniques that can be applied to different scenarios. These
techniques will be categorized and then compared for their advantages and disadvantages. Some
applications will be given as examples. The topics include but are not limited to
1. Optimization Formulation and Analysis
We discuss how to formulate the problem as an optimization issue. Specifically, we study what
the objectives are, what the parameters are, what the practical constraints are, and what the
optimized performances across the different layers are. The tradeoffs between the different
optimization goals and different users' interests are also investigated. The goal is to provide the
students a new perspective from the optimization point of view for variety of problems in
engineering fields.
2. Mathematical Programming
If the optimization problem is to find the best objective function within a constrained feasible
region, such a formulation is sometimes called a mathematical program. Many real-world and
theoretical problems can be modeled in this general framework. We discuss the four major
subfields of the mathematical programming: linear programming, convex programming, nonlinear
programming, and dynamic programming.
3. Integer/Combinatorial Optimization
The discrete optimization is the problem in which the decision variables assume discrete values
from a specified set. The combinatorial optimization problems, on the other hand, are problems of
choosing the best combination out of all possible combinations. Most combinatorial problems can
be formulated as integer programs. Integer optimization is the process of finding one or more best
(optimal) solutions in a well defined discrete problem space. The major difficulty with these
problems is that we do not have any optimality conditions to check if a given (feasible) solution is
optimal or not. We listed several possible solutions such as relaxation and decomposition,
enumeration, knapsack problem and cutting planes.
4. Game Theory
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COURSE SYLLABUS
Game theory is a branch of applied mathematics that uses models to study interactions with
formalized incentive structures (“games"). It studies the mathematical models of conflict and
cooperation among intelligent and rational decision makers. Rational means that each individual's
decision-making behavior is consistent with the maximization of subjective expected utility.
Intelligent means that each individual understands everything about the structure of the situation,
including the fact that others are intelligent rational decision makers. We have discussed four
different types of games, namely, the non-cooperative game, repeated game, cooperative game,
and auction theory. The basic concepts are listed and simple examples are illustrated.
Major Assignments/Exams
1. Two exams: One for convex optimization and one for game theory plus the other
optimization
2. Term project: one five page paper related to your research for optimization
3. Homework
Required Reading
1. Zhu Han, Dusit Niyato, Walid Saad, Tamer Basar, and Are Hjorungnes,Game
Theory in Wireless and Communication Networks: Theory, Models and
Applications, Cambridge University Press, UK, 2011.
2. Steven Boyd’s videos for convex optimization
3. Handout for parts of book, Zhu Han and K. J. Ray Liu, Resource Allocation for
Wireless Networks: Basics, Techniques, and Applications, Cambridge University
Press, 2008.
Recommended Reading
Some materials for other types of optimizations, which will be mentioned in the class.
List of discussion/lecture topics
All lecture notes can be found at http://www2.egr.uh.edu/~zhan2/
Grading Policy
Grades will be determined on the basis of exams, attendance, and submitted homework grades
with the following approximate weights. The actual weights will be fixed at the end of the
semester.
Attendance
Homework
Exams
Term project
5%
15%
40%
40%
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