# Foundations of numerical optimization

## General aims of the course

In optimization, the aim is to find the best, the minimum or maximum, solution to a problem formulated in mathematical terms.

There is often a vast freedom in how a practical problem can be cast as an optimization problem.

The participants will obtain an overview of a selection of important optimization methods as well as on how selected problems can be formulated as mathematical optimization problems.

This knowledge will in turn act as a guideline when addressing various problems in the participants’ own research.

## Course contents

The course is partitioned into three parts that aim to give the participants an introduction to (i) gradient based non-linear optimization, (ii) derivative free optimization, and (iii) optimization for differential equations.

## Learning outcomes

After completing the course you should be able to:

- define fundamental concepts within optimization,
- explain the underlying ideas behind important optimization methods,
- discuss fundamental optimization methods including strengths and weaknesses,
- reformulate a given problem as a mathematical optimization problem and solve it using a suitable optimization method.

## Examination

The examination consists of a number of homework assignments.

## Course schedule

**Week 43**(October 22-October 26): Preparatory work at home**Week 44**(October 29-November 2): Lectures and exercise sessions in Umeå (The first session starts Monday October 29 at 13:15 and the final session ends on Friday November 2 at 12:00.)**Week 45**(November 5-November 9): Homework

## Course responsible

Eddie Wadbro: eddie.wadbro@umu.se