PGMODAYS 2016

PGMODays 2016

 

Giuseppe Calafiore (Politechnico di Turino)

 Foundations and Recent Developments in Scenario Optimization

Scenario optimization has become a standard tool for tackling many robust design problems that are difficult to attack via standard, deterministic worst-case methods. In scenario design, a standard convex optimization problem with N randomly sampled constraints (the “scenarios”) is solved, and the scenario theory guarantees that the resulting solution is robust in a probabilistic sense against future realizations of the uncertainty. In this talk we will give an overview of the foundations of scenario optimization theory, and also discuss some recent developments and applications.

Biography

Presentation

Mérouane Debbah (Huawei)

Random Matrices for Engineering 5G

The asymptotic behavior of the eigenvalues of large random matrices has been extensively studied since the fifties. One of the first related result was the work of Eugène Wigner in 1955 who remarked that the eigenvalue distribution of a standard Gaussian hermitian matrix converges to a deterministic probability distribution called the semi-­‐circular law when the dimensions of the matrix converge to infinity. Since that time, the study of the eigenvalue distribution of random matrices has triggered numerous works, in the theoretical physics as well as probability theory communities. However, as far as communications systems are concerned, until the mid 90's, intensive simulations were thought to be the only technique to get some insight on how communications behave with many parameters. All this changed in 2000 when large system analysis based on random matrix theory was discovered as an appropriate tool to gain intuitive insight into communication systems. In particular, the self-­‐averaging effect of random matrices was shown to be able to capture the parameters of interest of communication schemes. Since then, the results led to very active research in many fields such as MIMO systems or Ultra-­‐Dense Networks. This talk is intended to give a comprehensive overview of random matrices and their application to the latest design of 5G Networks.

Biography

Patrick Jaillet (MIT)

Online Optimization for Dynamic Matching Markets

There are many situations in which present actions must be made and resources allocated with incomplete knowledge of the future. It is not clear in this setting how to measure the quality of a proposed decision strategy.  Online optimization compares the performance of a strategy that operates with no knowledge of the future (on-line) with the performance of an optimal strategy that has complete knowledge of the future (off-line). In some cases some probabilistic information about the future may be available. In this talk, we provide an overview of results obtained from that perspective on problems arising from dynamic matching markets such as (i) online auctions, (ii) display advertisements, and (iii) kidney exchange programs.

Biography

Presentation

Claire Mathieu (ENS)

The average diameter of social networks

"The friends of my friends are my friends". This well-known observation underlies a probabilistic model of social networks. With that model, one may explain the small world phenomenon: if one considers two a priori unrelated persons, in reality they can be related to each other by a short chain of friends. In a variant of the forest fire model, it is possible to prove this phenomenon rigorously.

Presentation

Michel PRENAT (Thales Optronique)

Thales Optronique : Optimization and related Data Analysis Problems

Thales Optronique SAS, part of Thales, is a leading company in the fields of optronic systems for defense applications (land, naval, airborne) and civil applications (high power lasers dedicated to scientific research and industrial processes), and radiofrequency systems for missile electronics applications. After a review of the applications and related skills, we show some optimization stakes in the fields of complex systems design, complex automatic functions, real time heterogeneous embedded computers, interface with the human operator, maintenance policy, databases acquisition. Some of these problems are a little bit more developed, showing a strong interaction between optimization and data analysis and processing.

Biography