# TMA4180 - Optimization 1

### Examination arrangement

Examination arrangement: Portfolio assessment

Evaluation form Weighting Duration Examination aids Grade deviation
work 30/100
Written examination 70/100 4 hours C

### 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.

### Further on evaluation

In the case that the student receives an F/Fail as a final grade after both ordinary and re-sit exam, then the student must retake the course in its entirety. Submitted work that counts towards the final grade will also have to be retaken. For more information about grading and evaluation. see «Teaching methods and activities».

### 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 2020

No.of lecture hours: 4
Lab hours: 1
No.of specialization hours: 7

Language of instruction: English, Norwegian

Location: Trondheim

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

Department of Mathematical Sciences

Phone:

# Examination

#### Examination arrangement: Portfolio assessment

Term Status code Evaluation form Weighting Examination aids Date Time Digital exam
Summer UTS work 30/100
Spring ORD work 30/100
Summer UTS Written examination 70/100 C
Spring ORD Written examination 70/100 C 2020-05-25 09:00
• * 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"

More on examinations at NTNU