Graduate School and Research Center in Digital Sciences

# Fundamentals of Optimisation

[Optim]
T Technical Teaching

## Abstract

Optimization is broadly applied to many technical and non-technical fields and  provides a powerful set of tools for the design and analysis of communication systems and signal processing algorithms. This course addresses basic concepts of optimization and will introduce EURECOM students to fundamental concepts as duality and KKT conditions, widely utilized optimization techniques as linear and geometric programming and unconstrained optimization algorithms,  but also to more advanced convex optimization techniques, which have been widely applied in wireless communications nowadays, such as second order cone programming and semidefinite programming.

Special emphasis is devoted to exemplify applications of optimization techniques to telecommunications problems with the objective of  developing skills and background necessary to recognize, formulate, and solve optimization problems.

Teaching and Learning Methods : Lectures supported by explicative exercises and dedicated exercise sessions

Course Policies : Attendance to exercise session is not mandatory but highly recommended.

## Bibliography

·         Sundaram, "A First Course in Optimization Theory", Cambridge University Press

·         Boyd and Vandenberghe, "Convex Optimization", Cambridge University Press

## Requirements

Basic knowledge in Linear Algebra and Real Analysis

## Description

·         Basic concepts of

o   Unconstrained optimization;

o   Optimization with equality constraints;

o   Constrained Optimization.

·         Algorithms for unconstrained minimization (descent methods, gradient and steepest descent methods, Newton method,...).

·         Convex set and convex and quasi-convex functions.

·         KKT conditions.

·         Duality.

·         Convex optimization

o   Linear optimization;

o   Geometric optimization;

o   Second-order cone programming;

o   Semidefinite programming.

Learning outcomes:

-      be able to recognize, formulate, and solve optimization problems.

-      be able to formulate a constrained optimization problem in terms of KKT conditions or in terms of primal and dual problem, solve this formulation being aware of its applicability limits.

-      be able to transform certain classes of problems in equivalent convex problems.

-      be able to understand the limits of application of techniques for  convex programming to nonconvex programming.

Nb hours:21.00 organized in 6 teaching sessions with at least 30% of the time (1 hour) dedicated to examples and explicative exercises and 1 dedicated exercise session (3 hours).

Grading Policy: maximum between and Final Exam(100%).

Nb hours: 21.00