Convex Optimization, 7.5 credits

Learning outcomes

Knowledge and understanding
After completing the course, the student must be able to
• understand the basic theoretical properties of convex optimization problems, and
• understand the basic properties of the main methods for solving convex optimization problem.

Skills and Abilities
After completing the course, the student must be able to
• set up optimization problems based on a real problem,
• identify different types of optimization problems, and
• apply basic methodology for numerical solution of convex optimization problems with computer tools.

Content

Theory of convex sets, functions and optimization problems. Theory for least squares problems and quadratic optimization. The simplex method and interior point methods. Duality and optimality conditions. Descent methods, Newton's method, line search. Applications in one or some of the areas signal processing, statistics, machine learning, control engineering, mechanical engineering or finance. Programming in MATLAB.

Examinations and grades

Examination, 7.5 credits (Code: A001)
Grades used are Fail (F), Sufficient (E), Satisfactory (D), Good (C), Very Good (B) or Excellent (A).

According to the Higher Education Ordinance, Chapter 6, Section 18, a grade is to be awarded on the completion of a course, unless otherwise prescribed by the university. The university may determine which grading system is to be used. The grade must be determined by a teacher specifically nominated by the university (the examiner).

In accordance with university regulations on grading systems for first and second-cycle courses and study programmes (Vice-Chancellor’s decision ORU 2018/00929), one of the following grades is to be used: fail (U), pass (G) or pass with distinction (VG). For courses included in an international master’s programme (60 or 120 credits) or offered to the university’s incoming exchange students, the A to F grading scale is to be used. The vice-chancellor, or a person appointed by them, may decide on exceptions from this provision for a specific course, if there are special grounds for doing so.

The grades used on this course are Fail (F), Sufficient (E), Satisfactory (D), Good (C), Very Good (B) or Excellent (A).

Modes of assessment

Examination (code A001): Written assignments

For students with a documented disability, the university may approve applications for adapted or other modes of assessment.

For further information, see the university's local examination regulations.

Specific entry requirements

Optimization, 7.5 Credits or Optimization for Students in Engineering, 7.5 Credis or Optimization for MSc in Engineering, 7.5 Credits.

For further information, see the university's admission regulations.

Other provisions

All or part of the course may be given in English.

Students who have been admitted to and registered on a course have the right to receive tuition and/or supervision for the duration of the time period specified for the particular course to which they were accepted (see, the university's admission regulations (in Swedish)). After that, the right to receive tuition and/or supervision expires.

Reading list and other learning resources

Required reading

Boyd, Stephen (2009)
Convex Optimization
Cambridge University Press
https://web.stanford.edu/~boyd/cvxbook/bv_cvxbook.pdf

Material handed out by the Mathematics unit.