ECTS credits ECTS credits: 5
ECTS Hours Rules/Memories Student's work ECTS: 85 Hours of tutorials: 5 Expository Class: 15 Interactive Classroom: 20 Total: 125
Use languages Spanish, Galician
Type: Ordinary subject Master’s Degree RD 1393/2007 - 822/2021
Departments: Statistics, Mathematical Analysis and Optimisation
Areas: Statistics and Operations Research
Center Faculty of Mathematics
Call: First Semester
Teaching: With teaching
Enrolment: Enrollable
The aim of this subject is to bring the student closer to the theoretical foundations of mathematical optimization, as well as to introduce applied aspects related to the modeling and resolution of optimization problems.
The objectives to be achieved as a result of learning are:
• Know in depth the differences between the different kinds of optimization problems.
• Know how to identify and model complex linear and non-linear optimization problems.
• Know the appropriate software to solve linear and non-linear optimization problems.
• Develop the necessary capabilities for the design of specialized optimization algorithms.
Unit 1. Introduction to convex analysis.
Unit 2. Convex optimization.
Unit 3. Languages for modeling optimization problems: AMPL
Unit 4. Optimization without constraints. Algorithms.
Unit 5. Optimization with constraints. Theoretical concepts.
Unit 6. Optimization with constraints.. Decomposition techniques.
Unit 7. Optimization with constraints. Classic algorithms.
Unit 8. Global Optimization.
Basic
- Bazaraa, M.S.; Sherali, H.; Shetty, C. (2006). “Nonlinear programming. Theory and algorithms”. Wiley.
- Ruszczynski, A.P. (2006). “Nonlinear optimization”. Princeton University Press.
- Horst, R.; Tuy, H. (2003). “Global Optimization: Deterministic Approaches”. Springer.
Complementary
- Fourer, R.; Gay, D.M.; Kernighan, B.W. (2002). “AMPL: A modeling language for Mathematical Programming”. Duxbury Press.
- Bertsekas, D.P. (2016). “Nonlinear programming”. Athena Scientific.
- Hiriart-Urruty, J.-B.; Lemaréchal, C. (2004). “Fundamentals of Convex Analysis”. Grundlehren Text Editions.
In this matter the basic, general and transversal competences collected in the memory of the title will be worked on. The specific competences that will be promoted in this area are indicated below:
E1 - Know, identify, model, study and solve complex statistical and operational research problems, in a scientific, technological or professional context, arising from real applications.
E3 - Acquire advanced knowledge of the theoretical foundations underlying the different methodologies of statistics and operational research, which allow for their specialized professional development.
E6 - Acquire advanced theoretical-practical knowledge of different mathematical techniques, specifically oriented to aid in decision-making, and develop reflective capacity to evaluate and decide between different perspectives in complex contexts.
E7 - Acquire advanced theoretical-practical knowledge of different mathematical optimization techniques, both in one-person and multi-person contexts, and know how to apply them with sufficient autonomy in a scientific, technological or professional context.
E9 - Know and know how to apply autonomously in scientific, technological or professional contexts, machine learning techniques and high-data analysis techniques (big data).
Most of the classroom teaching will consist of oral presentations by the teacher, among which some more practical sessions will be interspersed in which examples will be solved using specialized software, so it is necessary for students to have a computer in the classroom.
Activities will be proposed for students, which will consist of solving questions, exercises and examples related to modeling and solving applied optimization problems.
The appropriate support material will be provided to the student through the virtual campus.
The course will be divided into two parts, each with a weight of 50% in the final grade. This grade will come from 100% of continuous evaluation exercises, through the delivery and review of different works proposed throughout the course. In addition, in both parts there will be a theoretical-practical control that will also score for the continuous evaluation. The evaluation method will be the same in both the first and the second oportunities.
The exercises proposed in the continuous evaluation will be of a different nature, in order to evaluate the different competences to be developed in the subject:
- Theoretical-conceptual works will be assigned, in which the student must show their command of the concepts and contents developed in the expository classes. This will allow to evaluate the competences CB6, CB7, CB10, CG1, E3.
- Other works will require both modeling and solving optimization problems, followed by an analysis of the solutions obtained through structured and clear reports, which will allow the evaluation of the following additional skills CB8, CB9, CG2, CG4, CT1, CT3, CT4 , E1, E3, E6, E7, E9.
- In addition, some of these works will require the use of specific software and algorithms for their resolution, which will allow assessing CG5 proficiency and delving into E6.
- Finally, the CT5 competence will be developed by assigning some work to be done in a group.
Each ECTS credit translates into 7 hours of face-to-face class. It is estimated that the student will need, for each hour of face-to-face class, an additional hour for the global understanding of the contents. In addition, the continuous assessment work will amount to 10 hours per ECTS credit. In total 24 hours for ECTS credit will result.
It is convenient that the students have basic knowledge of mathematical optimization. It is also advisable to have average computer skills, and specifically specialized optimization problem modeling software.
Active participation in the learning process is recommended: attendance and participation in theoretical and practical classes. Use of tutorials and realization of a responsible effort of work and personal assimilation of the studied methods.
It is recommended that the student have completed a subject of Mathematical Programming in general and Linear and Integer Programming in particular.
In the development of the subject, it will be taken into account that the skills to be acquired must meet the MECES3 level. The predominant theoretical emphasis in this subject will be complemented by the study of some algebraic modeling language (such as AMPL or GAMS), which allows rapid prototyping and resolution of complex problems, as well as the agile implementation of specialized algorithms.
In cases of fraudulent performance of exercises or tests, the provisions of the respective regulations of the universities participating in the Master in Statistical Techniques will apply.
This guide and the criteria and methodologies described therein are subject to modifications arising from regulations and directives of the universities participating in the Master in Statistical Techniques.
Balbina Virginia Casas Mendez
Coordinador/a- Department
- Statistics, Mathematical Analysis and Optimisation
- Area
- Statistics and Operations Research
- Phone
- 881813180
- balbina.casas.mendez [at] usc.es
- Category
- Professor: University Lecturer
Julio Gonzalez Diaz
- Department
- Statistics, Mathematical Analysis and Optimisation
- Area
- Statistics and Operations Research
- Phone
- 881813207
- julio.gonzalez [at] usc.es
- Category
- Professor: University Lecturer
| 01.10.2025 16:00-20:00 | Grupo /CLE_01 | Classroom 04 |
| 06.23.2025 16:00-20:00 | Grupo /CLE_01 | Classroom 04 |