NMAK10012U Optimization and Convexity (OK)
MSc Programme in Mathematics
MSc Programme in Mathematics-Economics
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.
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
- Category
- Hours
- Exam
- 50
- Lectures
- 28
- Preparation
- 114
- Theory exercises
- 14
- Total
- 206
As
an exchange, guest and credit student - click here!
Continuing Education - click here!
- Credit
- 7,5 ECTS
- Type of assessment
- Oral examination, 30 minutesContinuous assessmentThe 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.
Course information
- Language
- English
- Course code
- NMAK10012U
- Credit
- 7,5 ECTS
- Level
- Full Degree Master
- Duration
- 1 block
- Placement
- Block 2
- Schedule
- A
- Course capacity
- No limits
- Continuing and further education
- Study board
- Study Board of Mathematics and Computer Science
Contracting department
- Department of Mathematical Sciences
Course responsibles
- Salvador Pineda Morente