Postgraduate Course: Fundamentals of Optimization (MATH11111)
Course Outline
School  School of Mathematics 
College  College of Science and Engineering 
Credit level (Normal year taken)  SCQF Level 11 (Postgraduate) 
Availability  Available to all students 
SCQF Credits  10 
ECTS Credits  5 
Summary  Classification of optimization problems; Convexity in optimization; Linear programming: Model formulation and assumptions; Graphical solution; Simplex method; Duality theory; Dual simplex method; Sensitivity analysis; Largescale linear programming; Unconstrained nonlinear optimization; Optimality conditions. 
Course description 
This course is designed to expose students to different types of optimization problems and to introduce appropriate solution approaches for each type. The role of convexity in optimization is emphasised. The course provides an indepth treatment of linear programming and solving linear programming problems using the simplex method. The students will be exposed to the theoretical foundations of linear programming problems. The role of duality and sensitivity analysis for linear programming problems are examined. Alternative solution approaches for largescale linear programming are discussed. The course gives a brief introduction to nonlinear optimization and introduces a few basic algorithms for unconstrained optimization. A tentative list of course topics is as follows: Introduction, taxonomy of optimization problems, basic examples Convex sets, convex functions, role of convexity in optimizationIntroduction to linear programming, graphical solution, standard form linearprogramming, vertices, simplex method in tableau form Twophase simplex method, infeasible and unbounded LPs Finite convergence of the simplex method Duality theory Dual simplex method Sensitivity analysis, economic interpretation of the dual problemLargescale linear programming, column generation, cutting plane methods Introduction to nonlinear optimization, optimality conditions Basic algorithms for unconstrained optimization

Entry Requirements (not applicable to Visiting Students)
Prerequisites 
Students MUST have passed:

Corequisites  
Prohibited Combinations  
Other requirements  None 
Information for Visiting Students
Prerequisites  None 
High Demand Course? 
Yes 
Course Delivery Information

Academic year 2022/23, Not available to visiting students (SS1)

Quota: None 
Course Start 
Semester 1 
Course Start Date 
19/09/2022 
Timetable 
Timetable 
Learning and Teaching activities (Further Info) 
Total Hours:
100
(
Lecture Hours 22,
Seminar/Tutorial Hours 12,
Summative Assessment Hours 2,
Programme Level Learning and Teaching Hours 2,
Directed Learning and Independent Learning Hours
62 )

Assessment (Further Info) 
Written Exam
60 %,
Coursework
40 %,
Practical Exam
0 %

Additional Information (Assessment) 
4 assessments (10% each, to be tentatively given out during Weeks 3, 5, 7, and 9) ¿each assessment will have a mix of STACK exercises and openended problems. STACK exercises will provide instant individual feedback to students. Openended problems will be marked by the course team. The first two learning outcomes will be assessed in each assessment as well as the written exam. The third learning outcome is expected to be assessed in the third and fourth assessments as the topic will be covered in the second half of the semester. 
Feedback 
Before each assessment, a problem set will be announced. Each problem set will have the same format as the following assessment, i.e., a combination of STACK exercises and openended problems. STACK exercises will provide instant individual feedback to students. Openended problems will be discussed during the workshop in the following week, virtual office hours,and possibly in the discussion forums. 
Exam Information 
Exam Diet 
Paper Name 
Hours & Minutes 

Main Exam Diet S1 (December)  Fundamentals of Optimization  2:00  
Learning Outcomes
On completion of this course, the student will be able to:
 Identify different types of optimization problems, and be able to connect these with the available methods for their solution.
 Apply appropriate optimization techniques to solve small optimization problems by hand.
 Discuss and interpret the sensitivity of a solution of an optimization problem to changes in the parameter values of the problem.

Reading List
Introduction to Linear Optimization, Dimitris Bertsimas and John N. Tsitsiklis, Athena Scientific, Dynamic Ideas, LLC, Belmont, Massachusetts, 1997, ISBN: 1886529191 Linear Programming: Foundations and Extensions, Robert J. Vanderbei; Fred Hillier (Editor); Robert J. Vanderbei (Editor), Springer US, Boston, Massachusetts, 2008, Third Edition, International Series in Operations Research & Management Science, ISBN: 0387743871 Linear Programming and Network Flows, Mokhtar S. Bazaraa, John J. Jarvis, Hanif D. Sherali, Hoboken, N.J, John Wiley & Sons, 2010, Fourth edition, ISBN: 0471485993Linear and Nonlinear Programming, David G. Luenberger, Yinyu Ye, Springer US, New York, NY, 2008, Third Edition, International Series in Operations Research & Management Science, ISBN: 0387745025 
Contacts
Course organiser  Prof Alper Yildirim
Tel: (0131 6)50 5271
Email: E.A.Yildirim@ed.ac.uk 
Course secretary  Miss Gemma Aitchison
Tel: (0131 6)50 9268
Email: Gemma.Aitchison@ed.ac.uk 

