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Kungl Tekniska högskolan / Optimization and Systems Theory /

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EL3300/SF3847 Convex optimization with engineering applications, 6cr

(The lecture notes will be updated during the course. They are not available yet.)

General information

This course is a graduate course, given jointly by the School of Electrical Engineering, and the Department of Mathematics at KTH. The course is primarily not intended for students with focus on optimization, but rather aimed for students from other areas.

Examiners: Anders Forsgren (Mathematics) and Mikael Johansson (Automatic Control).

The course consists of 24h lectures, given during Period 2, 2016.

Course literature: S. Boyd and L. Vandenberghe, Convex Optimization, Cambridge University Press, 2004, ISBN: 0521833787

Aim

After completed course, you will be able to

  • characterize fundamental aspects of convex optimization
    (convex functions, convex sets, convex optimization and duality);
  • characterize and formulate linear, quadratic, geometric and semidefinite programming problems;
  • implement, in a high level language such as Matlab, crude versions of modern methods for solving convex optimization problems, e.g., interior methods;
  • solve large-scale structured problems by decomposition techniques;
  • give examples of applications of convex optimization within statistics, communications, signal processing and control.

Syllabus

  • Convex sets
  • Convex functions
  • Convex optimization
  • Linear and quadratic programming
  • Geometric and semidefinite programming
  • Duality
  • Smooth unconstrained minimization
  • Sequential unconstrained minimization
  • Interior-point methods
  • Decomposition and large-scale optimization
  • Applications in estimation, data fitting, control and communications

Course requirements

For passing the course, successful completion of homework assignments and presentation of a research paper in a short lecture are required.

There will be a total of four sets of hand-ins distributed during the course. Late homework solutions are not accepted.

The short lecture should sum up the key ideas, techniques and results of a (course-related) research paper in a clear and understandable way to the other attendees.

Prerequisites

The course requires basic knowledge of calculus and linear algebra. Please contact the lecturers if you are uncertain about your prerequisities.

Schedule

Lectures will be given in Room 3721, Lindstedtsvägen 25, KTH.

Lecture notes can be found at the course's Canvas page.

Lecture Date  Time Venue Activity Lecturer
1 Tue Nov 1 13-15 Room 3721 Introduction AF/MJ
2 Thu Nov 3 10-12 Room 3721 Convexity AF
3 Mon Nov 7 10-12 Room 3721 Linear programming and the simplex method AF
4 Thu Nov 10 10-12 Room 3721 Lagrangian relaxation, duality and optimality for linearly constrained problems AF
5 Tue Nov 15 13-15 Room 3721 Sensitivity and multiobjective optimization MJ
6 Thu Nov 17 10-12 Room 3721 Convex programming and semidefinite programming AF
7 Tue Nov 22 8-10 Room 3721 Geometric programming and second-order cone programming MJ
8 Thu Nov 24 10-12 Room 3721 Smooth convex unconstrained and equality-constrained minimization AF
9 Tue Nov 29 13-15 Room 3721 Interior methods AF
10 Thu Dec 1 10-12 Room 3721 Decomposition and large-scale optimization MJ
11 Tue Dec 6 13-15 Room 3721 Applications in communications and control MJ
12 Thu Dec 8 10-12 Room 3721 Applications in communications and control MJ

Research paper presentations will be held on December 9.

Course web page

http://www.math.kth.se/optsyst/forskning/forskarutbildning/SF3847/

Optimization and Systems Theory, KTH
Anders Forsgren, andersf@kth.se