NDAA09009U Numerical Optimization
(NO)
Volume
2016/2017  Language  English   Credit  7,5 ECTS   Level  Full Degree Master   Duration  1 block   Placement  Block 3  Schedule  C   Course capacity  No limit  Continuing and further
education   Study board  Study Board of Mathematics and Computer
Science   Contracting department   Department of Computer Science
  Course responsible   Sune Darkner (76a677871746b78466a6f34717b346a71)
  Saved on the
13052016 
Education  MSc programme in Computer Science
MSc Programme in Bioinformatics 
Content  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 casestudy problems like
computing the motion of a robot hand or fitting a model to highly
nonlinear data or similar problems.
The topics covered during the course are:  First order optimality conditions, KarushKuhnTucker
Conditions, Taylors Theorem, Mean Value Theorem.
 Nonlinear Equation Solving: Newtons Method, etc..
 Linear Search Methods: Newton Methods, QuasiNewton Methods,
etc..
 Trust Region Methods: LevenbergMarquardt, Dog leg method,
etc..
 Linear Least squares fitting, Regression Problems, Normal
Equations, etc.
 And many more...
 Learning Outcome  Knowledge of:  Theory of gradient descent method
 Theory of Newton and Quasi Newton Methods
 Theory of Thrust Region Methods
 Theory of quadratic programming problems
 First order optimality conditions (KKT conditions)
Skills to:  Apply numerical optimization problems to solve unconstrained
and constrainted minimization problems and nonlinear root search
problems.
 Reformulate one problem type into another form such as root
search to minimization and vice versa
 Implement and test numerical optimization methods
Competences to:  Evaluate which numerical optimization methods are best suited
for solving a given optimization problem
 Understand the implications of theoretical theorems and being
able to analyze real problems on that basis
 Literature  See Absalon when the course is set up.  Teaching and learning methods  Mixture of study groups and project group work
with handins. 
Academic qualifications  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 Taylor's 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. 
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Exam  Credit  7,5 ECTS   Type of assessment  Continuous assessment The exam is based on 57 written assignments and at least one
oral presentation in class.   Marking scale  7point grading scale   Censorship form  No external censorship
Several internal examiners   Reexam  Re handingin of written assignments and a 15 minute oral
presentation without preparation.    Criteria for exam assesment  In order to achieve the highest grade 12, a student must be able
to  Derive Newton's method for nonlinear equations
 Derive Newton's 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.


Workload  Category  Hours  Exercises  72  Preparation  50  Project work  84  Total  206 

Saved on the
13052016

