Syllabus for |
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| TMA521 - Large scale optimization |
| Storskalig optimering |
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| Syllabus adopted 2020-02-18 by Head of Programme (or corresponding) |
| Owner: MPENM |
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7,5 Credits
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| Grading: TH - Pass with distinction (5), Pass with credit (4), Pass (3), Fail |
| Education cycle: Second-cycle |
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Major subject: Mathematics |
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Department: 11 - MATHEMATICAL SCIENCES
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Course round 1
Teaching language: English
Application code: 20149
Open for exchange students: Yes
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Credit distribution |
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Examination dates |
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Sp1 |
Sp2 |
Sp3 |
Sp4 |
Summer course |
No Sp |
| 0197 |
Examination |
7,5c |
Grading: TH |
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7,5c
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Contact examiner, |
Contact examiner, |
Contact examiner |
In programs
MPENM ENGINEERING MATHEMATICS AND COMPUTATIONAL SCIENCE, MSC PROGR, Year 1 (compulsory elective)
MPENM ENGINEERING MATHEMATICS AND COMPUTATIONAL SCIENCE, MSC PROGR, Year 2 (elective)
MPDSC DATA SCIENCE AND AI, MSC PROGR, Year 2 (elective)
MPDSC DATA SCIENCE AND AI, MSC PROGR, Year 1 (compulsory elective)
TKITE SOFTWARE ENGINEERING, Year 3 (elective)
TKITE SOFTWARE ENGINEERING, Year 2 (elective)
Examiner:
Ann-Brith Strömberg
Go to Course Homepage
Course round 2
Teaching language: English
Application code: 99223
Open for exchange students: No
Maximum participants: 20
Only students with the course round in the programme plan
| Module |
|
Credit distribution |
|
Examination dates |
|
Sp1 |
Sp2 |
Sp3 |
Sp4 |
Summer course |
No Sp |
| 0197 |
Examination |
7,5c |
Grading: TH |
|
|
7,5c
|
|
|
|
|
|
|
Examiner:
Ann-Brith Strömberg
Go to Course Homepage
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 decomposition–coordination (or, distributed algorithm–consensus); 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. Decomposition–coordination, 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, Dantzig–Wolfe 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.
Literature
See the course home page.
Examination including compulsory elements
Written reports and oral presentations of the projects; opposition/peer review; presence at workshops; a written exam