# TMA4180 - Optimization 1

### Examination arrangement

Examination arrangement: Aggregate score

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:

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 To
SIF5030 7.5
More on the course

Facts

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

Coursework

Term no.: 1
Teaching semester:  SPRING 2025

Language of instruction: English

Location: Trondheim

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

Department of Mathematical Sciences

# Examination

#### Examination arrangement: Aggregate score

Term Status code Evaluation Weighting Examination aids Date Time Examination system
Spring ORD School exam 70/100
Spring ORD Portfolio 30/100
Summer UTS School exam 70/100
• * 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.
Examination

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

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