# Optimization in Rn (2WO11)

## Announcements

The lectures start as planned on monday 22 april 2013.

There will be no lecture on thursday 25 april. Lecture 2 will take place on thursday 2 may. There will be an instruction on friday 26 april.

## Course materials

There are lecture notes (.pdf) containing the homework questions.

Students of the TU/e are licenced to make use of AIMMS, a package for modelling and solving optimization problems (the password for downloading AIMMS is given in Lecture 1). Here is the AIMMS one-hour tutorial for students, and here are some sample AIMMS problems (made by Cor Hurkens): the Facility Location Problem, and the Portfolio Selection Problem.

Here are some programs for graphing calculators. If you know of any other useful programs, please let me know.

## Examination

A detailed description of the final objectives of this course can be found in the appendix of the lecture notes. You do not get a grade or a bonus for homework. You may not refer to any books or use a laptop at the exam. The use of a graphing calculator is allowed.

Old exams (for the old version of this course):

Exam & solutions of March 13th 2003.

Exam & solutions of May 13th 2003.

Exam of July 5th 2004.

## Schedule and Homework (2013)

Lecture 1 (22/4). Introduction, notation, Fredholms Alternative. Slides here. A paper on the SET game

Instruction 1 (26/4). Home: Exercises 1,2,3,4 from the Introduction. Tutorial: Exercises 5,6,7,8 from the Introduction. Solutions to selected exercises are here.

Lecture 2 (2/5). Linear inequalities, Farkas' Lemma. Slides here.

Instruction 2 (3/5). Home:Exercises 3, 7, 11 (erratum: 'separated' must be 'strongly separated') , 13 from Chapter 1.Tutorial: 4, 5, 6, 24 from Chapter 1. Exercise 24 is hard; try to apply Corollary 11.1. Solutions to selected exercises are here.

Lecture 3 (6/5). Linear optimization duality. Slides here.

Instruction 3 (13/5). Home: Exercises 2, 7, 10 of Ch. 2. Tutorial: 5, 9, 13 of Ch. 2. Solutions to selected exercises are here.

Lecture 4 (16/5). Polyhedra and polytopes. Slides here. Here is a story about a regular polytope, the 120-cell.

Instruction 4 (17/5). Home: 1, 4, 5, 6 of Ch. 3. Tutorial: 11, 12, 14, 23 of Ch. 3. Solutions to selected exercises are here.

Lectures 5a (23/5) and 5b (27/5). The simplex method. Slides here.

Instruction 5 (30/5). Home: 2, 4, 5, 7 of Ch 4. Tutorial: 1, 8, 10 of Ch 4. Solutions to selected exercises are here.

Lecture 6 (6/6). Integer linear optimization. Slides here. Here is a story about a quadratic diophantine equation, the Pell equation.

Instruction 6 (7/6). Home: 1,3,6,8 of Ch. 5; 5 of Ch. 6. Tutorial: 9, 11, 13 of Ch. 5; 6, 9 of Ch. 6. Solutions to selected exercises are here.

Lectures 7a (10/6) and 7b (13/6). Semidefinite matrices and convex functions. Slides here.

Instruction 7 (14/6). Home:Exercise 2, 3, 4, 5, 6, 11 from Ch. 7. Tutorial: Exercise 10, 12, 13, 15, 16, 18, 23 from Ch 7. Solutions to selected exercises are here.

Lectures 8 (17/6). Convex optimization. Slides here.

Lecture 9 (20/6). Conic optimization and polynomials. Slides here.

Instruction 8 (21/6). Home: Exercise 1,2,4,5 from Ch. 8. Tutorial: Exercise 10, 11 from Ch. 8. Solutions to selected exercises are here.