# Nonlinear Optimization (2DE09)

## Announcements

Solutions to all exercises are available at the THOR desk.

After the lectures there will be time to discuss the homework exercises in the lecture room or in my office (Metaforum 4.104).

## Course materials

We use the book `Convex Optimization', Boyd and Vandenberghe, Cambridge University Press 2004. This book is available in electronic form here. See also this site. The course will cover most of chapters 2,3,4,5,9,11.

## Course objectives

Theory of convex sets, convex functions and constrained convex optimization. Some algorithms for unconstrained and constrained minimization problems.

## Examination

Written exam, with questions similar but not identical to homework exercises.

The points on the last exam were distributed over the topics of this course as follows: 40% convex sets and convex functions (questions 1-4), 30% optimality conditions and duality for convex optimization (questions 5-7), 20% optimization modelling (questions 8,9), 10% optimization algorithms (question 10). As opposed to these older exams, current exams have: 10% modelling and 20% optimization algorithms.

The assignments of week 9 each count for 1 point on the exam. Please hand in these assignments one week before the exam. I'll allow collaboration between at most two people on each assignment.

## Homework and slides

Lecture 1. Introduction. Exercises and reading: see slides.

Lecture 2. A matlab package. Download and install the package CVX. Here is an assignment and a solution.

Lecture 3. Semidefinite matrices. Exercises and reading: see slides. Here is a syllabus containing further explanation on semidefinite matrices in section 7.2.

Lecture 4. Convex sets I. Exercises and reading: see slides.

Lecture 5. Convex sets II. Exercises and reading: see slides. Here is a solution to the CVX assignment in the slides.

Lecture 6. Convex functions. Exercises and reading: see slides.

Lecture 7. Lagrange duality I. Exercises and reading: see slides.

Lecture 8. Lagrange duality II. Exercises and reading: see slides.

Lecture 9. Unconstrained minimization, self-concordant functions. Exercises and reading: see slides.. I will post two new bonus assignments here halfway quartile 1, each good for one point at the exam. (Here are some older bonus assignments ).

Lecture 10. Interior point methods I. Exercises and reading: see slides.

Lecture 11. Interior point methods II. Exercises and reading: see slides.