MM836: Convex analysis

Study Board of Science

Teaching language: Danish or English depending on the teacher, but English if international students are enrolled
EKA: N310051112, N310051102
Assessment: Second examiner: None, Second examiner: External
Grading: Pass/Fail, 7-point grading scale
Offered in: Odense
Offered in: Spring
Level: Master

STADS ID (UVA): N310051101
ECTS value: 5

Date of Approval: 01-11-2022


Duration: 1 semester

Version: Archive

Comment

Joint teaching with MM525: Convex Analysis (5 ECTS)

Entry requirements

The course cannot be taken if you have followed or passed MM525.

Academic preconditions

Students taking the course are expected to:
  • Be familiar
    with: systems of linear equations, matrices, determinants, vector
    spaces, scalar product and orthogonality, linear transformations,
    eigenvectors and eigenvalues, polynomials, the concept of a function and
    its derivatives, real numbers, vector calculus.

Course introduction

The course will introduce analytic techniques and geometrical concepts
in order to solve linear and non-linear optimization problems, mostly
 in economy.
The course builds on the knowledge acquired in
the courses MM505 Linear Algebra, or MM540, or MM538, and MM533
Mathematical and Numerical Analysis.

The course is of high
multidisciplinary value and gives an academic basis for a Bachelor
Project in several core areas of Natural Sciences and Economy.

In relation to the competence profile of the degree it is the explicit focus of the course to:
  • Give the competence to :handle complex and development-oriented situations in study and work contexts.
Give skills to:
  • apply the thinking and terminology from the subject's basic disciplines.
  • analyze and evaluate the theoretical and practical problems for the application of a suitable mathematical model.
Give knowledge and understanding of:
  • basic knowledge generation, theory and methods in mathematics
  • how to conduct analyses using mathematical methods and critically evaluate scientific theories and models.

Expected learning outcome

The learning objectives of the course is that the student demonstrates the ability to:
  1. Correctly answer written assignments and prove results within the syllabus of the course.
  2. Reproduce and illustrate definitions and results within the syllabus of the course.
  3. Formulate answers to written assignments in a mathematically correct language.
  4. Give arguments for the steps in the solution of the exercises.
  5. Compare key results within the syllabus of the course.
  6. Understand and identify the practical problems that can be solved with the methods in the course syllabus.
  7. Use the presented methods to solve practical optimization problems.

Content

The following main topics are contained in the course:
Convex
sets and their topology, convex functions, conjugation,
subdifferentiability, minimization, Kuhn-Tucker theory, Numerical
optimization methods.

Literature

See itslearning for syllabus lists and additional literature references.

Examination regulations

Exam element a)

Timing

Spring

Tests

Mandatory assignments

EKA

N310051112

Assessment

Second examiner: None

Grading

Pass/Fail

Identification

Full name and SDU username

Language

Normally, the same as teaching language

Examination aids

To be announced during the course

ECTS value

1

Exam element b)

Timing

June

Tests

Oral exam

EKA

N310051102

Assessment

Second examiner: External

Grading

7-point grading scale

Identification

Student Identification Card

Language

Normally, the same as teaching language

Duration

30 minutes

Examination aids

To be announced during the course

ECTS value

4

Indicative number of lessons

42 hours per semester

Teaching Method

Teaching activities are reflected in an estimated allocation of the workload of an average student as follows:

  • Intro phase (lectures) - 28 hours
  • Training phase: 14 hours

The intro phase will introduce general concepts and theory and exercise sessions will be devoted to learn material in depth. Interactive teaching will be used.

Educational activities 

  • preparation of exercises in study groups
  • preparation of projects

Teacher responsible

Name E-mail Department
Michele Della Morte dellamor@cp3.sdu.dk Computational Science

Timetable

Administrative Unit

Institut for Matematik og Datalogi (matematik)

Team at Educational Law & Registration

NAT

Offered in

Odense

Recommended course of study

Profile Education Semester Offer period

Transition rules

Transitional arrangements describe how a course replaces another course when changes are made to the course of study. 
If a transitional arrangement has been made for a course, it will be stated in the list. 
See transitional arrangements for all courses at the Faculty of Science.