NMAK10012U Optimization and Convexity (OK)

Volume 2014/2015
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:

- 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 under invigilation
The final grade of the student is weighed as follows:
- Each student must present at least 5 exercises and their final project in the class (30%)
- oral examination (70%)
Students must pass both parts to pass the overall exam.
Exam registration requirements
- The students must hand in a final project
Aid
Only certain aids allowed

Some written aid will be allowed during the oral examination

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

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.