Module Code
Module Title
Host Institution/
Contact
Pre-requisites
TGI_M06
Convex Optimization and an Introduction to Congestion Control
NUI Maynooth, Robert Shorten
ECTS
Chief Examiner
Teaching Staff
Delivery
Aims
Undergraduate multi-variable calculus and linear algebra, some knowledge of differential equations. All of the important mathematical concepts will be reviewed in class.
5
Prof. F. Wirth ,
Teaching methods: 24 hours of lectures, together with guided study assignments
July 2012

To present the basic concepts of convex optimization covering theory and algorithms; to present basic probability necessary to formulate congestion control problem; to present the application of convex optimization methods in the area of congestion control. To provide students with the background required to pursue independent research in these topics.
Target audience: first and second year PhD students in
Engineering and the Mathematical Sciences.

Syllabus
Assessment
Bibliography
1) Convexity of sets and functions
2) Convex Optimization Problems
3) Duality in Convex Optimization
4) Computational Methods
5) Basics of Probability Theory
6) Markov Processes
7) Relationship to Network Protocols
8) Continuous Time and Fluid Models
9) Basic Stability Tests
10) Congestion Control as a Resource Allocation Problem
11) Convex Games
12) Differential Equations Models
13) Optimal Congestion Control
14) Fairness Issues in Bandwidth Allocation
Assessment: one 2-hour examination
S.P. Boyd and L. Vandenberghe, Convex Optimization, Cambridge
University Press, 2004.
R. Skrikant, The mathematics of internet congestion control,
Birkhäuser, 2004.
M. Welzel, Network congestion control: Managing internet traffic.
J. Wiley, 2005.