Introduction to Mathematical Optimization: Course Information

Description

Optimization is at the heart of decision-making in engineering, science and economics, whenever the goal is the best design, the lowest cost or the most efficient use of resources. This module introduces the theory and practice of mathematical optimization, with a focus on convex problems that can be solved reliably and efficiently. It opens with a review of the mathematical toolkit: sets, logic, methods of proof, vector spaces, matrices, geometry and calculus. Students then learn to state unconstrained, equality-constrained and constrained optimization problems in standard form. The core of the module covers convex sets and functions, convex optimization problems such as linear and quadratic programming, and Lagrange duality with its geometric interpretation and optimality conditions. Students also study solution algorithms, including descent methods, Newton’s method and an introduction to interior-point methods. Hands-on tutorials with CVX, a MATLAB package for convex optimization, give practical experience in solving problems. Students should have a good working knowledge of linear algebra, multivariable calculus and probability. On completion, students will be able to define optimization problems mathematically, apply the fundamentals of convex analysis and solve basic convex optimization problems.

The main goal of the course is to teach students to formulate real-world problems as mathematical optimization problems, understand what makes them efficiently solvable, and solve them with sound theory and practical software tools.

Intended Audience

MSc students in areas of communication and networking

Course Textbook

• E. K. P. Chong and H. Stanislaw, An Introduction to Optimization, A John Wiley & Sons, Inc., Publication, 2013.

• C. D. Mayer, Matrix Analysis and Applied Linear Algebra, SIAM, 2000.

• S. Boyd and L. Vandenberghe, Convex Optimization. Cambridge, U.K. Cambridge Univ. Press, 2004

Lectures

30 hours of lectures and 15 hours of tutorials

Grading

• Standard university grading applies
  

• The course evaluation consists of

  • Assignments (30%)

  • Fnal examination: 70%

Course Learning Outcomes

After finishing the course, the attendant will

• Define a mathematical optimization problem.

• Apply basics of convex analysis, tools, and techniques to optimization problems.

• Solve basic convex optimization problems.

Working load

4h per Week + homework + viva sessions.

Credits

This is a 3 credit course.

Teaching and learning methodology

The lectures will be mainly based on blackboard and slides.

Prerequisites

Background in elementary analysis, basic linear algebra, and basic statistics.

Additional references

• D. P. Palomar and Y. C. Eldar, “Convex Optimization in Signal Processing and Communications,” Cambridge University Press, 2009.