Checking date: 27/04/2020

Course: 2019/2020

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 0. Introduction 1. Optimization and constraints 2. Convex versus non-convex optimization problems 3. On closed-form optimization: analytical versus algorithmic solutions 4. Types of optimization problems Unit 1. Quadratic Optimization 1. Problem formulation 2. Matrix and vector derivatives 3. Equality constraints 4. Lagrange multipliers Unit 2. Convex Optimization 1. Convex sets, functions and optimization problems 2. Lagrange duality and KKT conditions 3. Algorithms and optimization techniques 4. Lab: Disciplined convex programming: CVX Unit 3. Non-Convex Optimization 1. Global optimization: local minima versus global minima 2. Local optimization algorithms 3. Convex relaxation and approximate solutions 4. Majorization-minimization principle 5. Lab: TensorFlow Unit 4. Applications 1. Signal reconstruction and robust approximation 2. Optimization for machine learning 3. Low-rank optimization problems
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. - Lab 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

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