# Optimization II, 7.5 ECTS

Second level## Facts

No available facts**Course code**MM8015

## Syllabus

## Description

The focuses of the course are on the theory of convex sets and functions and its connection with a number of topics that span a broad range from continuous to discrete optimization. These topics include constraint qualification, Lagrange multiplier theory, Lagrangian and conjugate/ Fenchel duality, minimax theory and nondifferentiable optimization. In addition the following topics will be dealt with on demand: network programming, mathematical treatment of optimization algorithms, optimization in Hilbert spaces, application on sciences and mathematical economics and finance.

## Area of interests: Science and Mathematics

Science and mathematics help us understand how the world around us is connected – from the origin and structure of the universe, to the development and function of humanity and all other organisms on earth. Scientific knowledge makes it possible to critically examine the credibility of information in different areas of everyday life, society, and the media. As a scientist or mathematician, you will be attractive on a large job market that covers all parts of society and includes everything from pure technology companies to environment and healthcare, as well as research.

## Subject

### Mathematics

As a mathematical theory always implies that certain conclusions hold under certain given conditions, it can in principle say nothing about the physical reality. None the less mathematics has become an indispensable tool for a large number of subjects like astronomy, physics, chemistry, statistics and the technical sciences and in later times also for economy, biology, various social sciences and computor science. The role of mathematics in the applied sciences is both to supply notions for exact and adequate formulations of empirical laws but also from these laws to derive consequences, which can be used to find better models of the reality one has to describe. These tasks have lately become more important. Mathematics is in continual progress by intensive international research, new theories are created and already existing theories are simplified and augmented.