NMAK10012U Optimization and Convexity (OK)

Volume 2013/2014
Education
MSc Programme in Mathematics
MSc Programme in Statistics
MSc Programme in Mathematics-Economics
Content
This course aims at giving an introduction to convexity theory and its applications to optimization problems. The following basic topics are central to the subject: topological perperties of convex sets, cones, extreme points, separation, convex funtions, subdifferential calculus and the notion of conjugate duality.   We will develop the necessary and sufficient conditions of optimality for convex problems and we will also address some aspects of the duality theory.
Learning Outcome
Knowledge:
The student is supposed to get a good understanding of basic results in the theory of convex sets and convex functions. As examples are mentioned, separation theorems, duality and the conjugate of a convex function.

Skills:
The knowledge is applied to optimization problems and the student is supposed to be able to describe how the solution to such a problem may be obtained by an implementation of an algorithm, which in turn is based on convexity theory .
 
Competences:
The goal is that the student understands how theoretical problems from other sciences may be modelled and solved using optimization techniques coming from convexity theory.



.
Introductory courses in linear algebra and calculus (e.g. LinAlg and MatIntro). Analysis 1 (An1) (or similar) recommended.
4 hours of lectures and 2 hours og exercises/discussion per week
  • Category
  • Hours
  • Exam
  • 50
  • Lectures
  • 28
  • Preparation
  • 114
  • Theory exercises
  • 14
  • Total
  • 206
Credit
7,5 ECTS
Type of assessment
Written examination, 3 hrs under invigilation
The homeworks will be graded, and so will the final exam. The final grade is the average of these 2 grades.
Exam registration requirements
2 sets of exercises done as homework.
Aid
Only certain aids allowed
Only books and notes are allowed at the exam. The homeworks may be discussed with the other students, but the final formulations of the answers must be personal and made by the student alone. .
Marking scale
7-point grading scale
Censorship form
No external censorship
Exam period
One internal examiner
Re-exam
Reexamination: Oral, 30 minutes, with 30 minutes preparation time. Graded according to the 7 step scale with two internal examiners.
Criteria for exam assesment

The student must in a satisfactory way demonstrate that he/she has mastered the learning outcome.