TMA4180 - Optimization I


Examination arrangement

Examination arrangement: Portfolio assessment
Grade: Letters

Evaluation Weighting Duration Grade deviation Examination aids
Arbeider 30/100
Skriftlig eksamen 70/100 4 timer

Course content

First and second order necessary and sufficient (Karush-Kuhn-Tucker) optimality conditions for unconstrained and constrained optimization problems in finite-dimensional vector spaces. Basics of convex analysis and Lagrangian duality theory and their application to optimization problems and algorithms. An overview of modern optimization techniques and algorithms for smooth problems (including line-search/trust-region, quasi-Newton, interior point and active set methods, SQP and augmented Lagrangian approaches). Basic derivative-free and non-smooth optimization methods.

Learning outcome

The student successfully meeting the learning objectives of the course will be able to:
(i) assess the existence and uniqueness of solutions to a given optimization problem;
(ii) validate convexity of functions, sets, and optimization problems;
(iii) derive necessary and sufficient optimality conditions for a given optimization problem;
(iv) solve small optimization problems analytically;
(v) explain the underlying principles and limitations of modern techniques and algorithms for optimization;
(vi) estimate the rate of convergence and complexity requirements of various optimization algorithms;
(vii) implement optimization algorithms on a computer;
(viii) apply optimization algorithms to model problems in engineering and natural sciences.

Learning methods and activities

Lectures, exercises and semester assignment. Portfolio assessment is the basis for the grade awarded in the course. This portfolio comprises a written final examination (70%) and the semester assignment (30%). The grade for the whole portfolio (course grade) is given by the letter grading system. Retake of examination may be given as an oral examination. Lectures will be given in English if international master or exchange students want to attend the course. If the course is taught in English, the exam will be given only in English. Students are free to choose Norwegian or English for written assessments.

Course materials

Will be announced at the start of the course.

Credit reductions

Course code Reduction From To
SIF5030 7.5

Version: 1
Credits:  7.5 SP
Study level: Second degree level


Term no.: 1
Teaching semester:  SPRING 2017

Language of instruction: English, Norwegian


Subject area(s)
  • Mathematics
  • Technological subjects
Contact information
Course coordinator:
  • Markus Grasmair

Department with academic responsibility
Department of Mathematical Sciences


Examination arrangement: Portfolio assessment

Term Status code Evaluation Weighting Examination aids Date Time Examination system Room *
Spring ORD Arbeider 30/100
Room Building Number of candidates
Spring ORD Skriftlig eksamen 70/100 2017-05-27 09:00
Room Building Number of candidates
Summer KONT Arbeider 30/100
Room Building Number of candidates
Summer KONT Skriftlig eksamen 70/100 2017-08-11 09:00
Room Building Number of candidates
  • * The location (room) for a written examination is published 3 days before examination date. If more than one room is listed, you will find your room at Studentweb.

For more information regarding registration for examination and examination procedures, see "Innsida - Exams"

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