Optimization, 7.5 credits

Aims and objectives

General aims for first cycle education

First-cycle courses and study programmes shall develop:

• the ability of students to make independent and critical assessments
• the ability of students to identify, formulate and solve problems autonomously, and
• the preparedness of students to deal with changes in working life.

In addition to knowledge and skills in their field of study, students shall develop the ability to:

• gather and interpret information at a scholarly level
• stay abreast of the development of knowledge, and
• communicate their knowledge to others, including those who lack specialist knowledge in the field.

(Higher Education Act, Chapter 1, Section 8)

Course objectives

Knowledge and Understanding
After completed studies, the student shall have

• know about the most important problems in discrete and continuous optimization, and
• know and being able to use the most important methods for solving discrete and continuous optimization problems.

Competence and Skills
After completed studies, the student shall be able to
formulate an optimization problem from a real world,
recognize different types of optimization problems,
account for and use the most important concepts in optimization,
account for the fundamental theory and methods for linear programs, and
account for the fundamental theory and methods for the most important discrete and continuous optimization problems.

Main content of the course

The formulation of optimization problems. Global and local optimum. Constraints. Convexity. Line search methods. Linear programs with applications. The Simplex method. Duality. Integer and combinatorial optimization. Relaxation. Branch and bound. Branch and cut. Heuristic methods. Nonlinear programming with applications. Necessary and sufficient conditions for optimum. Gradient methods. Newtons method. Quasi-Newton methods. Nonlinear programming with constraints and applications. KKT-conditions. Projeced gradient methods. Linear and quadratic programs. Programming in Matlab and GAMS.

Teaching methods

Teaching is done in the form of lectures and computer exercises.
The teaching will be in the form of lectures and exercises in computer lab.

The teaching methods may be altered, should only a few students take the course.

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.

Examination methods

Theory, 4.5 credits (Code: A001)
Written exam.

Computer Assignments, 3 credits (Code: A002)
Assignments reported in writing and orally

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

For further information, see the university's local examination regulations (in Swedish).

Grades

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 prescribe which grading system shall apply. The grade is to be determined by a teacher specifically appointed by the university (an examiner).

According to regulations on grading systems for first- and second-cycle education (vice-chancellor's decision 2019-01-15, ORU 2019/00107), one of the following grades is to be used: fail, pass, or pass with distinction. The vice-chancellor or a person appointed by the vice-chancellor may decide on exceptions from this provision for a specific course, if there are special reasons.

Grades used on course are Fail (U), Pass (G) or Pass with Distinction (VG).

Theory
Grades used are Fail (U), Pass (G) or Pass with Distinction (VG).

Computer Assignments
Grades used are Fail (U), Pass (G) or Pass with Distinction (VG).

For further information, see the university's local examination regulations (in Swedish).

Specific entry requirements

Mathematical Modelling and Problem Solving, 7.5 Credits and Komplex Analysis, 7.5 Credits

For further information, see the university's admission regulations (in Swedish).

Transfer of credits for previous studies

Students who have previously completed higher education or other activities are, in accordance with the Higher Education Ordinance, entitled to have these credited towards the current programme, providing that the previous studies or activities meet certain criteria.

For further information, see the university's local credit transfer regulations (in Swedish).

Other provisions

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

Reading list and other teaching materials

Required Reading

Stephen Boyd (senaste upplagan)
Convex Optimization
Cambridge University Press
Nätupplaga finns att ladda ner utan kostnad, https://web.stanford.edu/~boyd/cvxbook/bv_cvxbook.pdf

Material som tillhandahålls av enheten för matematik.

Reference