Course syllabus

Information about the course in the KTH course directory: SF1861

What is optimization?

Optimization is about how to use mathematical models and numerical soultion methods to determine the best solution among a set of feasible alternatives.
In the mathematical model the alternatives are described with the help of a number of variables, for which there usually are several restrictions that in the model are described by so called constraints. To determine which is the best alternative the model needs a so called objective function, which for each alternative (characterized by the variables) gives a quantitative measure of how "good" this alternative is. Some common areas of applications are scheduling, route planning, portfolio management, optimal control and learning.

Intended learning outcomes

After completing the course students should for a passing grade be able to

Apply basic theory, concepts and methods, within the parts of optimization theory described by the course content, to solve problems
Formulate simplified application problems as optimization problems and solve using software.
Read and understand mathematical texts about for example, linear algebra, calculus and optimization and their applications, communicate mathematical reasoning and calculations in this area,orally and in writing in such a way that they are easy to follow.

For higher grades the student should also be able to

Explain, combine and analyze basic theory, concepts and methods within the parts of optimization theory described by the course content.

Course main content

Examples of applications of optimization and modelling training.

Basic concepts and theory for optimization, in particular theory for convex problems.

Linear algebra in Rⁿ^, in particular bases for the four fundamental subspaces corresponding to a given matrix, and LDL^T-factorization of a symmetric positive semidefinite matrix.

Linear optimization, including duality theory.

Optimization of flows in networks.

Quadratic optimization with linear equality constraints.

Linear least squares problems, in particular minimum norm solutions.

Unconstrained nonlinear optimization, in particular nonlinear least squares problems.

Optimality conditions for constrained nonlinear optimization, in particular for convex problems.

Lagrangian relaxation. (New from 2019)

Literature

The main literature is the compendium "Optimization" by Amol Sasane and Krister Svanberg (ASKS).

We also recommend the following book:

Linear and Nonlinear Optimization (Links to an external site.)Links to an external site., second edition, by I. Griva, S. G. Nash och A. Sofer, SIAM, 2009.
(The book can be ordered from several places. Please note that you can become a SIAM member for free (Links to an external site.)Links to an external site. and obtain a discount at the SIAM bookstore.)

For students who plan to continue and take the follow up courses SF2812 and SF2822 the book is used as the main literature in both of those courses.

Support for students with disabilities

Students with disabilities may have the right to certain compensatory support for example during examination.

KTH has coordinators for students with disabilities, Funka who deals with issues relating to functional disabilities. You should turn to Funka at funka@kth.se for information about support.

Examination

The examination is divided into to parts, mandatory home assignments corresponding to HEM1, and a written exam corresponding to TEN1. Details about the examination are given on canvas.