Numerical Optimisation (NO)

Numerical optimisation 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 optimisation like; inverse kinematics in robotics, image segmentation and registration in medical imaging, protein folding in computational biology, stock portfolio optimisation, motion planning and many more.

This course will build up a toolbox of numerical optimisation 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 of science.

This course teaches the basic theory of numerical optimisation methods. The focus is on deep understanding, and how the methods covered during the course works. Both on a theoretical level that goes into deriving the math but also on an implementational level focusing on computer science and good programming practice.

There will be weekly programming exercises where students will implement the algorithms and methods introduced from theory on their own case-study problems like computing the motion of a robot hand or fitting a model to highly non-linear data or similar problems.

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...