| TAOP07 |
Introduction to Optimization, 6 ECTS credits.
/Optimeringslära grundkurs/
For:
DAV
Mat
MED
Y
Yi
|
| |
Prel. scheduled
hours: 60
Rec. self-study hours: 100
|
| |
Area of Education: Science
Main field of studies: Mathematics, Applied Mathematics
|
| |
Advancement level
(G1, G2, A): G1
|
|
Aim:
Optimization deals with mathematical theory and methods aiming at analyzing and solving decision problems that arise in technology, economy, medicine, etc. The course gives a broad orientation of the field of optimization, with emphasis on basic theory and methods for continuous and discrete optimization problems in finite dimension, and it also gives some insight into its use for analyzing practical optimization problems. After the course, the student shall be able to:
- identify optimization problems and classify them according to their properties, into, for example, linear and nonlinear, or continuous and discrete, problems
- construct mathematical models of simple optimization problems
- define and use basic concepts, such as, for example, local and global optimality, convexity, weak and strong duality, and valid inequalities
- reproduce and apply basic theory for some common types of optimization problems, such as, for example, duality theory for linear optimization problems, and have knowledge about and be able to use optimality conditions, such as, for example, Bellman's
equations, to determine the optimality of a given solution
- describe and apply basic principles for solving some common types of optimization problems, such as, for example, branch-and-bound for discrete problems
- use relaxations, and especially Lagrangian duality, to approximate optimization problems, and be able to estimate the optimal objective value through lower and upper bounds
- use commonly available software for solving optimization problems of standard type.
|
|
Prerequisites: (valid for students admitted to programmes within which the course is offered)
Calculus, linear algebra, and Matlab
Note: Admission requirements for non-programme students usually also include admission requirements for the programme and threshhold requirements for progression within the programme, or corresponding.
|
|
Supplementary courses:
Optimization, advanced course Y, Applied optimization - project course, Mathematical optimization.
|
|
Organisation:
Lectures which include theory, problem solving and applications. Exercises which are intended to give individual training in problem solving. A laboratory course with emphasis on modelling and the use of optimization software.
|
|
Course contents:
Fundamental concepts within optimization, such as mathematical modelling, optimality conditions, convexity, sensitivity analysis, duality, and Lagrangean relaxation. Basic theory and methods for linear and nonlinear optimization, and integer and network optimization.
|
|
Course literature:
Jan Lundgren, Mikael Rönnqvist and Peter Värbrand: Optimeringslära (Studentlitteratur).
Exempelsamling: Optimeringslära grk for Y.
|
|
Examination: |
|
Written examination
Labratory course
|
5 ECTS
1 ECTS
|
| |
|
|
Course language is Swedish.
Department offering the course: MAI.
Director of Studies: Ingegerd Skoglund
Examiner: Torbjörn Larsson
Link to the course homepage at the department
Course Syllabus in Swedish
|
|