Warning

# AE4B33OPT -- Optimization (English Version) 2015-16

## News

• Exam will be at room G-205 on Tuesday Feb 2, 10pm. Please bring calculators and blank sheets. No notes allowed (both printed or hand-written).

## Overview

This course is about optimisation in finite-dimensional (Euclidean) spaces. It includes least squares problems, linear programming and convex optimisation. You will learn:

• to recognise and formulate a problem as an optimisation problem with or without constraints
• necessary and sufficient optimality conditions
• fundamentals of convex analysis
• some algorithms for solving optimisation problems.

## Lectures

Lecturer: Tomáš Werner

Schedule (may change during the term):

# date topic optional materials
01 02.10. Matrix algebra.
02 09.10. Recap of parts of linear algebra. EE263 lect. 2-4
03 16.10. Ortogonality, QR decomposition. EE263 lect. 4-5
04 23.10. Least squares, least norm. EE263 lect. 5-6,9
05 30.10. Quadratic functions, spectral decomposition. EE263 lect. 15-17
06 06.11. Quadratic functions, spectral decomposition.
07 13.11. SVD
08 20.11. Multivariate calculus.
09 27.11. Local extrema, free and equality-constrained. Luenberger 7.1-7.3, 11.1-11.4
10 04.12. Numerical algorithms to find free local extrema. Luenberger 8.8
11 11.12. Linear programming. Convex sets, convex polyhedra. Luenberger 2.1-2.6
12 18.12. Simplex method. Luenberger 3.1-3.5
13 08.01. Convex functions, convex optimization. EE364a lect. 3-4
14 15.01. Duality. EE364a lect. 5

Here are lecture notes (partially translated into English, the translation will gradually progress).

“Luenberger” refers to the book David Luenberger - Yinyu Ye: Linear and Nonlinear Programming.

Here is optional literature.

## Evaluation of the Course

The total number of points is the sum of:

• Lab homeworks: max. 50 points,
• Exam: max. 50 points.

Necessary condition for passing the course is passing the labs and min. 25 points from the exam. The final mark is then determined by the table:

 points mark [0,50) [50,60) [60,70) [70,80) [80,90) [90,100] F E D C B A 