Engineering Decision Theory: Course Information

Description

Many engineering decisions, from design and resource allocation to system operation, can be framed as optimization problems. This module gives students the mathematical foundations and practical tools to formulate and solve them. It begins with a review of vector and matrix algebra, including spectral decomposition, and of probability and statistics, covering sampling, hypothesis testing and multivariate techniques. Students learn to distinguish between deterministic and data-driven models. Optimization is then introduced as a decision-making tool from geometric, analytical and algorithmic viewpoints. The core of the module is convex optimization: convex sets and functions, duality, optimality conditions, and linear and quadratic models. Students then study solution algorithms, including descent methods, Newton’s method and interior-point methods. Practical work with the CVX modelling system lets students build and solve real optimization problems. On completion, students will be able to formulate engineering decision problems mathematically, choose and apply suitable optimization techniques, and use modern software tools to reach optimal or near-optimal decisions.

The main goal of the course is to equip students to formulate engineering decisions as optimization problems and solve them confidently using convex optimization theory, efficient algorithms and modern software tools.

Intended Audience

MSc students in areas of applied mathematics, communication, control, computer sciences, networking, civil engineering.

Course Textbook

• K. Binmore and J. Davies, Calculus, Cambridge University Press, 2012 Binmore-2012

• S. Boyd and L Vandenberghe, Introduction to Applied Linear Algebra Vectors, Matrices, and Least Squares, Cambridge University Press, 2018, Boyd-2018

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

• G. C. Calafiore and L. E. Ghaoui, Optimization Models, Cambridge University Press, 2014, Calafiore-2014

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

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

• R Hammack, Book of Proof, 2009, Hammack-2009

Lectures

4 hours/week, 14 to 15 weeks

Grading

• Standard university grading applies
  

• The course evaluation consists of

  • Assignments (20%)

  • Quizzez (10%)

  • Mid examination (20%)

  • Fnal examination: 50%

Course Learning Outcomes

After finishing the course, the attendant will

• Discriminate between deterministic and data-driven models.

• Apply linear algebraic and statistical concepts to formulate optimization problems in decision making.

• Make optimal/suboptimal decisions for a given problem by using appropriate optimization techniques.

• Manipulate the state-of-the-art optimization software tools.

Working load

4h per Week + homework + viva sessions.

Credits

This is a 4 credit course.

Teaching and learning methodology

The lectures will be mainly based on blackboard and slides.

Prerequisites

Background in elementary analysis, linear algebra, and statistics.