NMAK10012U Optimization and Convexity (OK)
MSc Programme in Statistics
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
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Continuing Education - click here!
- Credit
- 7,5 ECTS
- Type of assessment
- Oral examination, 30 minutes under invigilationThe 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.
Course information
- Language
- English
- Course code
- NMAK10012U
- Credit
- 7,5 ECTS
- Level
- Full Degree Master
- Duration
- 1 block
- Placement
- Block 2
- Schedule
- A (Tues 8-12 + Thurs 8-17)
- 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
Lecturers
Salvador Pineda Morente