Course Syllabus for

# Numerical Optimization Numerisk optimering

## FMA275F, 7.5 credits

Valid from: Autumn 2015
Decided by: FN1/AndersGustafsson
Date of establishment: 2016-02-17

## General Information

Division: Mathematics
Course type: Third-cycle course
Teaching language: English

## Aim

The aim of the course is to give good knowledge about modern numerical optimization algorithms especially about those suitable for large-scale problems - in particular their practical strengths and weaknesses and a deeper understanding of the basic principles behind them - in order to be able to use them in research.

## Goals

Knowledge and Understanding

For a passing grade the doctoral student must

• be able to describe the main features of modern optimization algorithms which are used in practice.
• be able to explain the basic principles for the algorithms that are covered by the course.
• be able to describe the differences between algorithms with respect to properties and behaviour.

Competences and Skills

For a passing grade the doctoral student must

• be able to independently identify and formalize problems relevant for industry or research as optimization problems.
• show good ability to analyse an optimization problem and suggest a suitable numerical algorithm as well as to implement it in MATLAB.
• be able to give a qualitative comparison of the strengths and weaknesses of different numerical algorithms within the course (with respect to convergence, speed, stability, large-scale properties etc).
• be able to present a solution to mathematical problems within the course scope that is terminologically adequate, well structured and logically correct.

## Course Contents

Line search and trust-region methods, conjugate gradient and quasi-Newton methods, large-scale optimization, derivative-free methods, least-squares, nonlinear equations, theory and fundamentals of algorithms for nonlinear optimization with constraints, interior-point methods, quadratic and sequential quadratic programming, penalty and augmented Lagrangian methods.

## Course Literature

Nocedal, J. & Wright, S.: Numerical Optimization. Springer, 2006. ISBN 9780387303031.

## Instruction Details

Type of instruction: Seminars. Seminars by the course participants

## Examination Details

Examination formats: Written assignments, seminars given by participants