Course - Optimization 1 - TMA4180
TMA4180 - Optimization 1
About
Examination arrangement
Examination arrangement: Aggregate score
Grade: Letter grades
Evaluation | Weighting | Duration | Grade deviation | Examination aids |
---|---|---|---|---|
School exam | 70/100 | 4 hours | C | |
Portfolio | 30/100 |
Course content
This course provides an introduction to continuous optimization in finite dimensional vector spaces.
Topics to be discussed are: 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 convex duality theory and their application to optimization problems and algorithms. An overview of modern optimization techniques and algorithms for smooth problems (including Newton and quasi-Newton methods for unconstrained optimization; algorithms for linear programming; SQP). Basic algorithms for non-smooth convex optimization problems. Introduction to vector optimization.
Learning outcome
The student successfully meeting the learning objectives of the course will be able to:
- assess the existence and uniqueness of solutions to a given optimization problem;
- validate convexity of functions, sets, and optimization problems;
- derive necessary and sufficient optimality conditions for a given optimization problem;
- use dual methods for the solution of convex optimization problems;
- understand solution concepts in vector optimization;
- solve small optimization problems analytically;
- explain the underlying principles and limitations of modern techniques and algorithms for optimization;
- estimate the rate of convergence and complexity requirements of various optimization algorithms;
- implement optimization algorithms on a computer;
- apply optimization algorithms to model problems in engineering and natural sciences.
Learning methods and activities
Lectures, exercises and project. The final grade is composed of a written exam (70%) and a portfolio of project work (30%).
Further on evaluation
In order to pass the course, a passing grade (A-E) in the written exam is required. In case of a retake of the course, all the course parts have to be taken again. The re-sit examination for the written exam may be given as an oral examination. The re-sit exam is in August. There will be no re-sit examination for the portfolio. Students are free to choose Norwegian or English for written assessments or the portfolio.
Recommended previous knowledge
Calculus 1-4, or equivalent.
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 2025
Language of instruction: English
Location: Trondheim
- Mathematics
- Technological subjects
Department with academic responsibility
Department of Mathematical Sciences
Examination
Examination arrangement: Aggregate score
- Term Status code Evaluation Weighting Examination aids Date Time Examination system Room *
- Spring ORD School exam 70/100 C 2025-05-06 09:00 INSPERA
-
Room Building Number of candidates SL410 orange sone Sluppenvegen 14 53 - Spring ORD Portfolio 30/100 INSPERA
-
Room Building Number of candidates - Summer UTS School exam 70/100 C INSPERA
-
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"