|Subject Area||Signals, Communications, and Networking|
|Semester||Semester 8 – Spring|
- Optimization theory: Introduction to optimization, classification of Optimization problems, Feasible Solutions, Optimal Solutions. Convex sets, Convex hulls. Convex and Concave functions. Elements of calculus and functions of several variables. Necessary and sufficient conditions for Local Optima. Search for optimum in one or many dimensions. Newton algorithm. Unconstrained optimization. Iterative Gradient methods. Steepest Descent methods, properties, convergence. Linear Programming overview: basic problem, set of feasible solutions. The Simplex algorithm. Duality. Dual problem, interpretation, Complementary Slackness conditions. Constrained Optimization. Problems with equality and inequality constraints, Kuhn- Tucker conditions. Convex function optimization-global optima. Dual Lagrange problem, Lagrangian relaxation of constraints. General Primal – Dual algorithm. Distributed optimization algorithms. Introduction to Game theory.
- Applications of Optimization theory. Sensor network design. Advanced transmission methods. Smart Antennas. Wireless ad-hoc networks: Routing, Scheduling, Energy management. Optimal control of PHY layer transmission e.g Transmission power and Rate. Network layer protocols (routing) and Transport layer protocols. Optimization-driven Flow control. General Primal – Dual algorithm, Peer-to-peer networks. Network resource pricing. Applications from Wireless network security.
The course focuses on theoretical description of optimization techniques and their application in communication systems. In the first part of the course the student is introduced to the concepts of linear programming and convex optimization. Next, particular emphasis is given to the formulation of problems that are amenable to convex optimization. One of the most important goals of the course is the understanding of ways to deal with problems that are not amenable to convex optimization. Throughout the course all the concepts are analyzed and explained through problems focused in the area of communication systems.
After successfully completing the course the student will be in a position to:
- Use linear programming algorithms and formulation techniques for solving a given problem
- Use convex optimization but also formulate problems as convex optimization problems.
- Solve problems with tools like Matlab/CPLEX/cvx.
- To formulate communication systems problems as optimization problems
The previous learning outcomes will be evaluated through problems that will be solved by the students (homework) but also through a problems that is focused on communication systems. In the project the student will be asked to solve a problem from a research publication. The project, the homework, but also the final exam, are designed so that they evaluate the student with respect to the previously described learning outcomes.