Checking date: 30/06/2020

Course: 2020/2021

Study: Master in Information Health Engineering (359)

Coordinating teacher: VAZQUEZ VILAR, GONZALO

Department assigned to the subject: Department of Signal and Communications Theory

Type: Electives
ECTS Credits: 6.0 ECTS


Students are expected to have completed
Students are expected to have a solid background in - Linear Algebra Prior knowledge on optimization is not required.
Competences and skills that will be acquired and learning results.
- Develop a solid theoretical basis for solving convex optimization problems arising in industry and research. - Learn manipulations to unveil the hidden convexity of optimization problems and relaxation techniques to treat non-convex optimization problems. - Be able to characterize the solution of convex and non-convex optimization problems either analytically or algorithmically. - Learn the usage of some of the more popular optimization toolboxes.
Description of contents: programme
Optimization theory is nowadays a well-developed area, both in the theoretical and practical aspects. This graduate course introduces the basic theory for solving optimization problems and illustrates its use with many recent applications in signal processing, communication systems and machine learning. · Course contents Unit 1. Introduction - Optimization problems and constraints - On closed-form optimization: analytical versus algorithmic solutions - Types of optimization problems - Applied linear algebra Unit 2. Quadratic Optimization - Problem formulation - Matrix and vector derivatives - Equality constraints - Duality and Lagrange multipliers Unit 3. Convex Optimization - Convex sets and convex functions - Convex and non-convex optimization problems - Lagrange duality and KKT conditions - Disciplined convex programming, CVX Unit 4. Optimization Algorithms - Local optimization algorithms - Stochastic optimization - Convex relaxation and approximate solutions Unit 5. Applications - Optimization for research
Learning activities and methodology
- Theoretical sessions: theoretical basis of optimization theory, illustrated with different applications and examples. Material for out-of-class work. - Problem sessions: formulation and solution of exercises motivated by different problems from communications, signal processing and machine learning. - Practical sessions: popular toolboxes for convex and non-convex optimization. The proposed projects will be solved in Matlab and/or Python programming environments.
Assessment System
  • % end-of-term-examination 0
  • % of continuous assessment (assigments, laboratory, practicals...) 100
Basic Bibliography
  • S. Boyd and L. Vandenberghe. Convex Optimization. Cambridge University Press. 2004
Recursos electrónicosElectronic Resources *
Additional Bibliography
  • A. Zhang, Z. C. Lipton, M. Li and A. J. Smola. Dive into Deep Learning. Online interactive book: 2019
  • S. Boyd and L. Vandenberghe. Introduction to Applied Linear Algebra - Vectors, Matrices, and Least Squares. Cambridge University Press. 2018
Recursos electrónicosElectronic Resources *
  • A. Zhang, Z.C. Lipton, M. Li and A.J. Smola · Dive into Deep Learning :
  • S. Boyd and L. Vandenberghe · Introduction to Applied Linear Algebra - Vectors, Matrices, and Least Squares :
(*) Access to some electronic resources may be restricted to members of the university community and require validation through Campus Global. If you try to connect from outside of the University you will need to set up a VPN

The course syllabus and the academic weekly planning may change due academic events or other reasons.