NMAK10012U Optimization and Convexity (OK)

Volume 2015/2016
Education

MSc Programme in Mathematics
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:

- Definition, properties and types of convex sets
- Definition, properties and types of convex functions
- Definition, properties, and solving of convex optimization problems
- Definition of Lagrangian duality and conditions for optimality
- Aplications and solutions algorithms of convex optimiation problems

The course provides tools and methods useful in other operations research related courses, such as OR2, stochastic programming course, etc.

The final project will aim to adress problems presented in other courses such as portfolio optimization or investment decisions.

Learning Outcome

 

Knowledge:
- To define the concepts of a convex set, a convex function, and a convex optimization problem
- To explain the properties of convex sets, convex functions and convex optimization problems
- To explain the concept and properties of the dual formulation of an optimization problem

Skills:
- To determine whether a given set, function, or optimization problem are convex
- To formulate the dual problem of a given optimization problem
- To solve a convex optimization problem using different algorithms
- To demonstrate the most relevant mathematical proofs concerning convex optimization

Competences:
- To formulate optimization problems of different fields
- To identify whether an optimization problem is a convex problem
- To evaluate the most appropiate methodology to solve a given convex optimization problem
- To use commercial software to solve convex optimization problems

 

Convex optimization by S. Boyd and L. Vandenbarghe

Introductory courses in linear algebra and calculus (e.g. LinAlg and MatIntro). Analysis 1 (An1) (or similar) recommended.
2x2 hours of lectures and 2 hours og exercises/discussion per weekfor 7 weeks.
  • Category
  • Hours
  • Exam
  • 50
  • Lectures
  • 28
  • Preparation
  • 114
  • Theory exercises
  • 14
  • Total
  • 206
Credit
7,5 ECTS
Type of assessment
Oral examination, 30 minutes
Continuous assessment
The final grade of the student is weighed as follows:
- Each student must present at least 5 exercises and a final project in the class (30%)
- Oral examination (70%)
Students must pass both parts to pass the overall exam.
The oral exam is 30 minutes with 30 minutes preparation time.
Aid
Only certain aids allowed

For the exercises and the project all aids are allowed.

For the oral exam  all aids are allowed during the preparation time, no aids are allowed during the examination.

Marking scale
7-point grading scale
Censorship form
No external censorship
One internal examiner for the continuous part and several internal examiners for the oral examination.
Re-exam

Only non-passed elements can be reexamined:
- If a student don't pass the presentation of 5 exercises and the final project, he/she must hand in a final project two weeks before the re-exam week and give a 1 hour presentation of 5 exercises and the final project before the re-examination.
- If the student don't pass the oral exam, he/she must take an oral re-exam identical to the ordinary oral exam
Passed element will be transferred with the original points.

Criteria for exam assesment

In the oral examination, the students must in a satisfactory way demonstrate that they:

- have accomplished the learning objectives of the course

- can explain the resolution of the exercises proposed througout the course

- can present the methodology and results of the final project

In order to pass the continous assessment the students must in a satisfactory way present in the class at least five exercises as well as the final project.