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Syllabus for

Academic year
TMA946 - Applied optimization
 
Owner: TM
5,0 Credits (ECTS 7,5)
Grading: TH - Five, Four, Three, Not passed
Level: A
Department: 0702 - Matematik MV CTH/GU


Teaching language: Swedish

Course module   Credit distribution   Examination dates
Sp1 Sp2 Sp3 Sp4 No Sp
0100 Examination 5,0 c Grading: TH   5,0 c    

In programs

TKBIA BIOENGINEERING, Year 4 (elective)
TTFYA ENGINEERING PHYSICS, Year 4 (elective)
TDATA COMPUTER SCIENCE AND ENGINEERING, Year 3 (elective)
TDATA COMPUTER SCIENCE AND ENGINEERING - Algorithms, Year 4 (compulsory)
TM Teknisk matematik, Year 1 (compulsory)
TM Teknisk matematik, Year 2 (compulsory)
TELTA ELECTRICAL ENGINEERING, Year 3 (elective)
TELTA ELECTRICAL ENGINEERING, Year 4 (elective)
TAUTA AUTOMATION AND MECHATRONICS ENGENEERING, Year 4 (elective)
TKEFA CHEMICAL ENGINEERING WITH ENGINEERING PHYSICS, Year 4 (elective)
EMMAS MSc PROGR IN ENGINEERING MATHEMATICS, Year 1 (compulsory)

Examiner:




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Eligibility:

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

Aim

The course is an introductory course in optimiza-tion. It serves to provide (1) basic knowledge of important classes of optimization problems and application areas of optimization models and methodologies; (2) practice in describing relevant parts of a real-world problem in a mathematical optimization model; (3) knowledge of and insights into the basic mathematical theory which underlies the principles of optimality; (4) examples of optimization methods that have been and can be developed from this theory in order to solve practical optimization problems.

Content

The course is broad in its context but the main focus is on optimization in continuous variables, which can be further divided into linear and non-linear optimization. A brief overview is also given of three other important areas of optimization: integer programming, network optimization, and optimiza-tion under uncertainty.
Outline of content: Mathematical modelling; local and global optimality; convex sets and functions; linear programming geometry and algebra; the simplex method; duality; linear programming soft-ware; integer programming modelling; implicit enumeration; heuristics; graph theory; minimum cost network flows; search methods; gradient methods; the KKT conditions for local optimal in constrained optimization; relaxations; Lagrangian duality; penalty and barrier methods,
Computer exercises: The course includes two com-puter exercises which are made by the use of optimization software. The firts concerns the simp-lex method and duality in linear programming, while the second concerns gradient methods in uncon- strained optimization, penalty and barrier methods, and the KKT conditions in constrained optimization.
Project: A case study, which serves to provide practice in the modelling and solving of a large optimization problem, to be able to answer relevant questions about the problem and its model solution, and to be able to give a nontechnical account of the problem and its solution in writing.

Literature

S.G. Nash and A. Sofer, Linear and nonlinear programming, McGraw-Hill, 1996

Examination

Compulsory computer exercises and a project, and a written exam combining theory and problem solution.


Page manager Published: Thu 03 Nov 2022.