Fundamentals of Optimisation

Abstract

• Convex 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 and main techniques in linear, non-linear and convex optimization.
• Special emphasis is devoted to exemplify their applications to telecommunications problems with the objective of developing the skills and background needed to recognize, formulate, and solve optimization problems.
• The course aims to introduce Eurecom students to fundamental concepts as duality and KKT conditions, widely utilized techniques as linear and geometric programming and unconstrained optimization algorithms, but also to more advanced techniques, which have been widely applied in wireless communications nowadays, namely, second order cone programming and semi definite programming.

Bibliography

Stephen Boyd and Lieven Vandenberghe, "Convex Optimization", Cambridge University Press, 2007, New York (USA)

Description

CONTENTS

• Convex set and convex functions;
• Convex optimization
• Linear optimization
• Geometric optimization
• Duality
• KKT conditions
• Algorithms for unconstrained minimization (descent methods, gradient and steepest descent methods, Newton method,...)
• Second-order cone programming

Semidefinite programming