Course contents *

Examples of applications and modelling training. Basic concepts and theory for optimization, in particular theory for convex problems. Some linear algebra in R^n, in particular bases for the four fundamental subspaces corresponding to a given matrix, and LDLT-factorization of a symmetric definite matrix. Linear optimization, including duality theory. Optimization of flows in networks. Quadratic optimization with linear 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.

Intended learning outcomes *

The overall purpose of the course is that the student should get well acquainted with basic concepts, theory, models and solution methods for optimization. Further, the student should get basic skills in modelling and computer based solving of various applied optimization problems.

Course Disposition

No information inserted

Specific prerequisites *

In general:

Completed upper secondary education including documented proficiency in English corresponding to English B. And 28 university credits (hp) in mathematics.

More precisely for KTH students:

Passed courses in calculus, linear algebra, differential equations, mathematical statistics, numerical analysis.

Recommended prerequisites

The student should have documented knowledge corresponding to university courses in mathematical calculus and analysis, linear algebra, numerical analysis, differential equations and transforms, and mathematical statistics.

Equipment

No information inserted

Literature

Linear and Nonlinear Programming by Nash and Sofer, McGraw-Hill, and some lecture notes.

Grading scale *

A, B, C, D, E, FX, F

Examination *

• TEN1 - Examination, 6.0 credits, Grading scale: A, B, C, D, E, FX, F

Based on recommendation from KTH’s coordinator for disabilities, the examiner will decide how to adapt an examination for students with documented disability.

The examiner may apply another examination format when re-examining individual students.

Other requirements for final grade *

A written examination (TEN1; 6 hp). Optional homeworks give credit points on the exam.

Opportunity to complete the requirements via supplementary examination

No information inserted

Opportunity to raise an approved grade via renewed examination

No information inserted

Examiner

Per Enqvist

Course web

Further information about the course can be found on the Course web at the link below. Information on the Course web will later be moved to this site.

Offered by

SCI/Mathematics

Main field of study *

Mathematics, Technology

Education cycle *

First cycle

Add-on studies

SF2812, SF2822.

Ethical approach *

• All members of a group are responsible for the group's work.
• In any assessment, every student shall honestly disclose any help received and sources used.
• In an oral assessment, every student shall be able to present and answer questions about the entire assignment and solution.

Supplementary information

SF1841 is today identical to SF1811, with common lectures and examination.