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MM836: Convex analysis (5 ECTS)

STADS: 13015101

Level
Master's level course

Teaching period
The course is offered in the spring semester.

Teacher responsible
Email: dellamor@cp3.dias.sdu.dk

Timetable
Group Type Day Time Classroom Weeks Comment
Common I Tuesday 08-10 U69A 6
Common I Tuesday 08-10 U157 7-12
Common I Thursday 08-10 U69A 5-12
H1 TE Monday 10-12 U69A 8
H1 TE Tuesday 10-12 U69A 6
H1 TE Tuesday 10-12 U17 8,10-11
H1 TE Tuesday 10-12 U143 9
H1 TE Tuesday 10-12 U8 12
H1 TE Tuesday 10-12 U60 14
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Comment:
Ubegrænset deltagerantal. Fælles undervisning med MM525

Prerequisites:
None

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.
 


Subject overview
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
    Meddeles ved kursets start


Website
This course uses e-learn (blackboard).

Prerequisites for participating in the exam
None

Assessment and marking:
  1. Mandatory assignments. Pass/fail, internal assessment by teacher. 0 ECTS
  2. Oral exam with all the use of all usual means of aid. Grades according to the 7-point grading scale, external grading. 5 ECTS

Reexam in the same exam period or immediately thereafter. The reexam may be a different type than the ordinary exam.



Expected working hours
The teaching method is based on three phase model.
Intro phase: 28 hours
Skills training phase: 14 hours, hereof:
 - Tutorials: 14 hours

Educational activities
  • preparation of exercises in study groups
  • preparation of projects
 
Educational form
Lectures will introduce general concepts and theory and exercise sessions will be devoted to learn material in depth. Interactive teaching will be used.

Language
This course is taught in Danish or English, depending on the lecturer. However, if international students participate, the teaching language will always be English.

Course enrollment
See deadline of enrolment.

Tuition fees for single courses
See fees for single courses.