course-details-portlet

TMA4180

Optimization 1

Choose study year
Credits 7.5
Level Second degree level
Course start Spring 2025
Duration 1 semester
Language of instruction English
Location Trondheim
Examination arrangement Aggregate score

About

About the course

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:

  1. assess the existence and uniqueness of solutions to a given optimization problem;
  2. validate convexity of functions, sets, and optimization problems;
  3. derive necessary and sufficient optimality conditions for a given optimization problem;
  4. use dual methods for the solution of convex optimization problems;
  5. understand solution concepts in vector optimization;
  6. solve small optimization problems analytically;
  7. explain the underlying principles and limitations of modern techniques and algorithms for optimization;
  8. estimate the rate of convergence and complexity requirements of various optimization algorithms;
  9. implement optimization algorithms on a computer;
  10. 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.

Course materials

Will be announced at the start of the course.

Credit reductions

Course code Reduction From
SIF5030 7.5 sp
This course has academic overlap with the course in the table above. If you take overlapping courses, you will receive a credit reduction in the course where you have the lowest grade. If the grades are the same, the reduction will be applied to the course completed most recently.

Subject areas

  • Mathematics
  • Technological subjects

Contact information

Course coordinator

Department with academic responsibility

Department of Mathematical Sciences