Course syllabus adopted 2023-02-14 by Head of Programme (or corresponding).
Overview
- Swedish nameStorskalig optimering
- CodeTMA522
- Credits7.5 Credits
- OwnerMPENM
- Education cycleSecond-cycle
- Main field of studyMathematics
- DepartmentMATHEMATICAL SCIENCES
- GradingTH - Pass with distinction (5), Pass with credit (4), Pass (3), Fail
Course round 1
- Teaching language English
- Application code 20138
- Open for exchange studentsYes
Credit distribution
Module | Sp1 | Sp2 | Sp3 | Sp4 | Summer | Not Sp | Examination dates |
|---|---|---|---|---|---|---|---|
| 0122 Examination, part A 6 c Grading: TH | 6 c |
| |||||
| 0222 Project, part B 1.5 c Grading: UG | 1.5 c |
In programmes
- MPDSC - DATA SCIENCE AND AI, MSC PROGR, Year 1 (compulsory elective)
- MPDSC - DATA SCIENCE AND AI, MSC PROGR, Year 2 (elective)
- MPENM - ENGINEERING MATHEMATICS AND COMPUTATIONAL SCIENCE, MSC PROGR, Year 1 (compulsory elective)
- TKITE - SOFTWARE ENGINEERING, Year 2 (elective)
- TKITE - SOFTWARE ENGINEERING, Year 3 (elective)
Examiner
Ann-Brith Strömberg- Full Professor, Applied Mathematics and Statistics, Mathematical Sciences
Eligibility
General entry requirements for Master's level (second cycle)Applicants enrolled in a programme at Chalmers where the course is included in the study programme are exempted from fulfilling the requirements above.
Specific entry requirements
English 6 (or by other approved means with the equivalent proficiency level)Applicants enrolled in a programme at Chalmers where the course is included in the study programme are exempted from fulfilling the requirements above.
Course specific prerequisites
Basic courses on linear and integer optimization as well as nonlinear optimization.Aim
The purpose of the course is to provide the students with an overview of the most important principles for the efficient solution of practical large-scale optimization problems, from modelling to method implementation. The course comprises a series of lectures covering theory and methodology, modelling exercises in smaller groups, and project assignments in which the students apply the knowledge gained to efficiently solve some relevant optimization problems.Learning outcomes (after completion of the course the student should be able to)
- independently analyze and suggest modelling and solution principles for large-scale complex optimization problems;
- have sufficient knowledge to use these principles successfully in practice through the use of computation software for optimization problems.
Content
Large-scale optimization problems often possess some inherent structures that can be exploited in order to solve such problems efficiently. The course deals with a number of such principles through which large-scale optimization problems can be attacked. A common term for such techniques is decompositioncoordination (or, distributed algorithmconsensus); convexity and duality theory underlie its development. The course includes practical moments: exercises in the modelling and solution of optimization problems with complicating constraints and/or variables, and project assignments in which large-scale optimization problems are to be solved through the use of duality theory and techniques presented during the lectures.
Contents in brief: complexity, simple/difficult optimization problems, integer linear optimization problems, unimodularity, convexity. Decompositioncoordination, restriction, relaxation, bounds on the optimal value, projection, variable fixing, dualization, neighbourhoods, heuristics, local search methods. Lagrangean duality, subgradient methods, (ergodic) convergence, recovery of integer solutions, Lagrangean heuristics, cutting planes, column generation, coordinating master problem, DantzigWolfe decomposition, Benders decomposition.
Organisation
Lectures. Modelling exercises including oral presentations and discussions. Project assignments including oral and written presentations as well as oppositions. Advisement. Mandatory presence at workshops. Additionally, there might be voluntary elements that could give bonus points for the written exam.
Literature
See the course home page.
Examination including compulsory elements
Written reports and oral presentations of the projects, which may also give bonus points on the exam; opposition/peer review; presence and active participation at workshops; a written exam.
The course examiner may assess individual students in other ways than what is stated above if there are special reasons for doing so, for example if a student has a decision from Chalmers on educational support due to disability.