|
| Udgave: |
Efterår 2012 NAT |
| Point: |
7,5 |
| Blokstruktur: |
2. blok |
| Skemagruppe: |
C |
| Fagområde: |
dat |
| Varighed: |
8 weeks |
| Omfang: |
On a weekly basis it is expected that the average workload on this course is about 20-25 hours. |
| Institutter: |
Computer Science |
| Studieordning: |
Master of Compter Science |
| Uddannelsesdel: |
Kandidat niveau |
| Kontaktpersoner: |
Kenny Erleben. Phone: 35.32.14.13, E-mail:kenny@diku.dk |
| Andre undervisere: |
Sune Darkner |
| Skema- oplysninger: |
 Vis skema for kurset
Samlet oversigt over tid og sted for alle kurser inden for Lektionsplan for Det Naturvidenskabelige Fakultet Efterår 2012 NAT |
| Undervisnings- form: |
Mixture of lectures, study groups and project group work with hand-ins. |
| Formål: |
Numerical optimization is a useful computer tool in many disciplines like image processing, computer vision, machine learning, bioinformatics, eScience, scientific computing and computational physics, computer animation and many more. A wide range of problems can be solved using numerical optimization like: inverse kinematics in robotics, image segmentation and registration in medial imaging, protein folding in computational biology, stock portfolio optimization, motion planing and many more.
This course will build up a toolbox of numerical optimization methods which the student can use when building solutions in his or her future studies. Therefore this course is an ideal supplement for students coming from many different fields in science.
This course teaches the basic theory of numerical optimization methods. The focus is on deep learning of how the methods covered during the course works. Both on a theoretical level that goes into deriving the math but also on an implementation level with focus on computer science and good programming practice.
There will be weekly programming exercises where students will implement the algorithms and methods introduced from theory and apply their own implementations to case-study problems like computing the motion of a robot hand or fitting a model to highly non-linear data or similar problems. |
| Indhold: |
The topics covered during the course are:
- First order optimality conditions, Karush-Kuhn-Tucker Conditions, Taylors Theorem, Mean Value Theorem.
- Nonlinear Equation Solving: Newtons Method, etc..
- Linear Search Methods: Newton Methods, Quasi-Newton Methods, etc..
- Trust Region Methods: Levenberg-Marquardt, Dog leg method, etc..
- Linear Least squares fitting, Regression Problems, Normal Equations, etc.
- And many more...
|
| Målbeskrivelse: |
In order to achieve the highest grade 12, a student must be able to
- Derive Newtons method for nonlinear equations
- Derive Newtons method for constrained minimization problems
- Derive first order optimality conditions for a minimization problem
- Implement computer programs that can solve the selected problems presented during the course.
- Account for how the selected problems presented during the course is reformulated into mathematical models such as nonlinear equations or constrained minimization problems.
|
| Lærebøger: |
Expected to be: Jorge Nocedal and Stephen J. Wright: Numerical Optimization, Springer |
| Tilmelding: |
Via KUnet from May 15th to the June 1st. |
| Faglige forudsætninger: |
It is expected that students know how to install and use Matlab by themselves. It is also expected that students know what matrices and vectors are and that students are able to differentiate vector functions.
Theorems like fundamental theorem of calculus, mean value theorem or Taylors theorem will be touched upon during the course. The inquisitive students may find more in depth knowledge from Chapters 2, 3, 5, 6 and 13 of R. A. Adams, Calculus, 3rd ed. Addison Wesley. |
| Eksamensform: |
Continious evaluation with grading according to the 7-step scale using internal grading based on written assignments and oral presentation in class.
Reexam: 20 minutes oral exam without preparation. |
| Eksamen: |
Løbende evaluering.
Reeksamen: Mundtlig prøve den 17. april 2013.
|
| Kursus hjemmeside: |
 |
| Undervisnings- sprog: |
Kun engelsk
|
| Sidst redigeret: |
24/5-2012 |