DAMSL-201 Optimization

Type

Elective

Course Code

DAMSL-201

Teaching Semester

B or C Semester

ECTS Credits

Student Performance Evaluation

Homework and/or Lab Assignments, Final Exam and/or Project

Prerequisite Courses

Calculus, Linear Algebra

Syllabus

First and second derivatives of a function of several real variables.
Extrema of functions: Lagrange multipliers.
Extrema of functions: consideration of the second derivatives
Extrema of functions: convex functions (general definition without differentiation, characterisation of convex functions, local and global minima of convex functions, quadratic functions and positive definite matrices).
Newton’s method
General results on nonlinear optimisation problems
Relaxation and gradient methods for unconstrained problems
Conjugate gradient methods for unconstrained problems
Relaxation, gradient and penalty-function methods for constrained problems
The Kuhn-Tucker conditions
Lagrangians and saddle points. Introduction to duality

Learning Outcomes

The course aims to provide students with the theoretical knowledge and practical skills necessary to formulate and solve optimisation problems in various computer science contexts. The objectives of the course are

familiarity with the formulation of optimisation problems
the necessary background in mathematical analysis techniques
an understanding of the practical application of the techniques to real systems.

Students’ familiarity with these topics will be reinforced through the application of established methods in the context of exercises, as well as the preparation of a project aimed at familiarising and presenting textual and experimental analysis techniques.