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Syllabus for

Academic year
TMA136 - Optimization under uncertainty
 
Owner: TM
5,0 Credits (ECTS 7,5)
Grading: TH - Five, Four, Three, Not passed
Level: C
Department: 11 - MATHEMATICAL SCIENCES


Teaching language: English

Course module   Credit distribution   Examination dates
Sp1 Sp2 Sp3 Sp4 No Sp
0101 Examination 5,0 c Grading: TH   5,0 c   Contact examiner

In programs

EMMAS MSc PROGR IN ENGINEERING MATHEMATICS, Year 1 (elective)
TTFYA ENGINEERING PHYSICS, Year 4 (elective)
TM Teknisk matematik, Year 2 (elective)
TITEA SOFTWARE ENGINEERING, Year 3 (elective)
TDATA COMPUTER SCIENCE AND ENGINEERING, Year 3 (elective)
TDATA COMPUTER SCIENCE AND ENGINEERING - Algorithms, Year 4 (elective)

Examiner:

Professor  Michael Patriksson



Eligibility:

For single subject courses within Chalmers programmes the same eligibility requirements apply, as to the programme(s) that the course is part of.

Course specific prerequisites

Basic knowledge of linear and nonlinear optimiza-tion and in probability theory.

Aim

The course constitutes a basic course in optimiza-tion under uncertainty (or, stochastic programming). It gives insigh into practical problems arising in quantitative decisions within economics, community planning and engineering sciences within which it is of importance to consider uncertain information; examples are given via recently published research articles.
The course provides knowledge about the modelling of decision problems with uncertain information as stochastic optimization problems, it illustrates the weight and importance of considering this type of modelling, and presents examples of methods for the efficient solution of the resulting optimization problems. The course also provides knowledge about and understanding of the basic mathematical theory that is relevant for this type of models.

Content

The course mainly considers stochastic optimiza-tion problems in continuous varibles but also prob-lems with integrality restrictions on the variables.
Outline of content: Linear programming (review), convexity and optimality, examples of the presence of uncertainties in applications of optimization, elementary terms in probabilty theory (review; sto-chastic variables, distributions, expected value), modelling of risk, decision stages, two stage prob-lem, recourse problem, deterministic equivalent model, discretization of distribution, scenarios, sce-nario tree, examples of recourse structures, appli-cation to practical optimization problems (e.g., electricity prodution, production planning and the design of electrical networks), the value of using a stochastic optimization model. decomposition methods for two-stage problems, stochastic quasi-gradient methods, probabilistic constraints, connec-tions with other models for decision problems under uncertainty, stochastic integer models.

Literature

P. Kall and S.W. Wallace, Stochastic Program-ming, Wiley, Chichester, 1994
W.K. Klein Haneveld and M.H. van der Vlerk, Stochastic Programming, University of Groningen, 2000
Journal articles..

Examination

Computer laborations and project exercises. And oral examination.


Page manager Published: Mon 28 Nov 2016.