Informasjons- og kommunikasjonsteknologi, masterprogram
Informasjons- og kommunikasjonsteknologi, 5-årig masterprogram
MA-430-G Probability Theory and Stochastic Processes. Linear Algebra, Mathematical analysis and basic Matlab programming.
The focus of the course is to provide in depth study of optimization tools in the context of important problems related to various engineering applications. On the one hand, these are very useful tools in order to understand, model and analyze correctly real problems, and on the other hand, these are also the key tools to design optimal or close-to-optimal solutions for these problems. The course covers the following topics: convex sets and convex functions, linear and quadratic programming, semidefinite programming, minmax, duality, Pareto optimization, dynamic programming and sequential optimization, interior-point methods, alternating projections, decomposition methods and distributed algorithms, introduction to non-convex optimization, discrete optimization, integer programming, relaxation methods, approximation algorithms and heuristics. The various optimization techniques will be continuously illustrated to solve important engineering problems in different areas, such as approximation and fitting, statistical signal processing, classification, problems on graphs and communication networks, control, computational geometry, data mining/analytics, machine learning, task scheduling and portfolio optimization.
Upon successful completion of the course, the students should
- have acquired the mentality and language of optimization
- know how to recognize, model and formulate real engineering problems as optimization problems
- understand the underlying theory, concepts and properties related to each of the optimization tools, especially those that are useful for computing solutions efficiently
- be able to design, implement and simulate practical algorithms to solve the various optimization problems
- be able to analyze the structures of problems and associated solutions, as well as the relationships between different problems
Arbeidsformer og arbeidsomfang
Lectures, exercises, self-study and group work. The work load for the average student is approximately 200 hours.
Course evaluation is carried out as a midterm evaluation in accordance with standard procedure in the quality assurance system, chapter 2.1.1. If necessary, a possible end of semester evaluation may be implemented.
The evaluation will consist of two parts:
a) Portfolio (25 %), where some of the exercises will be mini-projects. Information about the portfolio will be given in Fronter at the startup of the course.
b) Final written exam 3 hours (75 %). Graded assessment.