Optimization Methods

CourseT-810-OPTI
Semester20243
ETCS8
CoreNo

Year1. year
SemesterFall 2024
Level of course4. Second cycle, introductory
Type of courseElective
PrerequisitesT-403-ADGE, Operation Research
ScheduleNo schedule found.
Lecturer
Eyjólfur Ingi Ásgeirsson
Content
Level of course:                  3. Undergraduate (First cycle), advanced / 4. Graduate (Second cycle), introductory.
Type of course:                   Core in MSc Engineering Management and MSc Financial Engineering, elective in other  programmes.
Mandatory prerequisites: Operation Research (T-403-ADGE).Overview and approach: This course introduces the principal algorithms for linear, network, discrete, nonlinear, dynamic optimization and optimal control. Emphasis is on methodology and the underlying mathematical structures. Topics include the simplex method, network flow methods, branch and bound and cutting plane methods for discrete optimization, optimality conditions for nonlinear optimization, interior point methods for convex optimization, Newton´s method, heuristic methods, and dynamic programming and optimal control methods.Reading material:  Hillier and Lieberman, Introduction to Operations Research, 10th Edition, Pearson 2014.
Learning outcome - Objectives
 After the completion of this course students will be capable of using basic methods of Operations Research for analysing and solving complex decision problems. More specifically the student will be able to:  
  • Understand the properties of linear optimization and how it can be used to analyze and solve complex decision problems;
  • Use and analyze different forms of linear optimization models;
  • Understand and be capable of analyzing the geometry of linear optimization;
  • Apply systematic methods and algoirthms for analysing and solving decision problems;
  • Understand the importance and usefullness of linear optimization and its applications;
  • Apply software to solve optimization models;
  • Implement solution methods for linear optimization models and have in-depth understanding of the mechanics of the Simplex methods;
  • Practice the use of sensitivity analysis and to derive formulas for sensitivity of model parameters;
  • Understand integer programming and how it can used in decision making;
  • Use the main solution methods for integer programming;
  • Understand the special properties of network models and formulate practical problems as network models;
  • Understand the nature of non-linear optimization problems and the challenges involved in solving the problems;
  • Be familiar with different classes on non-linear optimization models and some of the available solution methods and algorithms; 
  • Understand the importance of optimization under uncertainty and be able to develop robust programming, change constraints and stochastic programming models;
  • Be familiar with dynamic programming; 
  • Present results in a clear and organized manner.
Course assessment
Final exam, mid-term exams, group based project, attendance and participation, homework.
Reading material
No reading material found.
Teaching and learning activities
Taught for 12 weeks. Lectures, exercises, group work, individual homework, mid-term exams, final exam.
Language of instructionEnglish