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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:

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


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


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