MSc in Electrical Engineering

Course Information Package

Course Unit TitleOPTIMIZATION METHODS AND APPLICATIONS
Course Unit CodeAEEE556
Course Unit DetailsMSc Electrical Engineering (Technical Electives) -
Number of ECTS credits allocated7
Learning Outcomes of the course unitBy the end of the course, the students should be able to:
  1. Explain the significance of optimization in engineering and develop, formulate and solve linear and nonlinear programming problems.
  2. Understand the concepts of constrained and unconstrained optimization, existence and uniqueness of optimal solutions, optimality conditions, convexity, feasibility and duality.
  3. Transform practical optimization problems into linear programming problems and solve them using the simplex method.
  4. Transform primal optimization problems into their dual and solve them using the dual simplex method.
  5. Transform practical optimization problems into nonlinear programming problems and solve them using the gradient method and the Newton method.
  6. Formulate and solve problems such as the transportation problem, the assignment problem, the minimum-cost flow problem, the maximal flow problem.
Mode of DeliveryFace-to-face
PrerequisitesNONECo-requisitesNONE
Recommended optional program components

 

Course Contents

Linear Programming: The standard form of the linear programming problem, slack variables, the manufacturing problem, the transportation problem, the routing problem, the scheduling problem, revision on linear algebra, linear dependence, Gaussian elimination, existence and uniqueness of optimal solutions, extreme points, vertices, basic solutions, basic feasible solutions and degeneracy, the fundamental theorem of linear programming.

 

The Simplex Method: The full tableau implementation of the simplex method.

 

Duality: Transformation of primal linear programming problems into the dual problems. The duality theorem, simplex multipliers, sensitivity and complementary slackness. The dual simplex method.  

 

Practical Optimization Problems: The assignment problem, the transportation problem, the minimum-cost flow problem and the maximal flow problem.

 

Unconstrained Non-Linear Programming: The standard form of the nonlinear programming problem, convexity, existence and uniqueness of optimal solutions, necessary and sufficient conditions for optimality, gradient methods, steepest descent method, Newton’s method, least squares problem, curve fitting, adaptive control, neural networks.

 

Constrained Non-Linear Programming:  Existence and uniqueness of optimal solutions, necessary and sufficient conditions for optimality, Conditional gradient methods.

 

Recommended and/or required reading:
Textbooks
  • David. G. Luenberger, Linear and Nonlinear Programming, Addison-Wesley, 1984.
References
  • D. P. Bertsekas, Nonlinear Programming, Athena Scientific, 1999.
  • D. Bertsimas, J.N. Tsitsiklis, Introduction to Linear Optimization, Athena Scientific, 1997.
Planned learning activities and teaching methods

Teaching is based on lectures.

The course delivery will be based on theoretical lecturing, assignments and exercises solved in class. Exercises will be handed to students and their solutions shall be analysed at lecture periods. Additional tutorial time at the end of each lecture will be provided to students. Students are expected to demonstrate the necessary effort to become confident with the different concepts and topics of the course.
Assessment methods and criteria
Assignments10%
Tests30%
Final Exam60%
Language of instructionEnglish
Work placement(s)NO