All Years Seminars
[INMA] 2015-12-01 (14:00) : Numerical Optimal Transport and Applications
At Euler building (A002)
Speaker :
Peyré, Gabriel
Abstract : Optimal transport (OT) has become a fundamental mathematical theoretical tool at the interface between calculus of variations, partial differential equations and probability. It took however much more time for this notion to become mainstream in numerical applications. This situation is in large part due to the high computational cost of the underlying optimization problems. There is however a recent wave of activity on the use of OT-related methods in fields as diverse as computer vision, computer graphics, statistical inference, machine learning and image processing. In this talk, I will review an emerging class of numerical approaches for the approximate resolution of OT-based optimization problems. These methods make use of an entropic regularization of the functionals to be minimized, in order to unleash the power of optimization algorithms based on Bregman-divergences geometry. This results in fast, simple and highly parallelizable algorithms, in sharp contrast with traditional solvers based on the geometry of linear programming. For instance, they allow for the first time to compute barycenters (according to OT distances) of probability distributions discretized on computational 2-D and 3-D grids with millions of points. This offers a new perspective for the application of OT in machine learning (to perform clustering or classification of bag-of-features data representations) and imaging sciences (to perform color transfer or shape and texture morphing). These algorithms also enable the computation of gradient flows for the OT metric, and can thus for instance be applied to simulate crowd motions with congestion constraints. This is a joint work with J.D. Benamou, G. Carlier, M. Cuturi and L. Nenna.
[INMA] 2015-11-24 (13:00) : Robust Power System Stability Assessment with Extensions to Inertia Control
At Euler building (A002)
Speaker :
Spyros Chatzivasileiadis (Massachusetts Institute of Technology
)
Abstract :
Security assessment of large-scale, strongly nonlinear power grids is an extremely computationally expensive task. Targeting at reducing this computational cost, we present a framework for constructing a robust assessment toolbox that can provide mathematically rigorous certificates of the grid stability with respect to the variations in system parameters and the grids ability to withstand a set of faults. By this toolbox we can off-line screen a wide range of contingencies in practice, without reassessing the system stability on a regular basis. In particular, we present two novel robust stability and resiliency problems of power grids subject to the uncertainty in equilibrium points and uncertainty in fault-on dynamics. In that, we bring in the quadratic Lyapunov functions approach to transient stability assessment. We extend these techniques further to address the optimal inertia allocation problem in order to guarantee the stability of low-inertia systems. We illustrate our techniques by numerical examples.
[INMA] 2015-11-17 (14:00) : Dynamical behavior of a stochastic proximal point algorithm
At Euler building (A002)
Speaker :
Pascal Bianchi (Télécom ParisTech)
Abstract :
Maximal monotone operators are set-valued mappings which extend (but are not limited to) the notion of subdifferential of a convex function.
The proximal point algorithm and the forward-backward algorithm are amongst the most studied algorithms for finding iteratively a zero of a sum
of two maximal monotone operators A and B. The purpose of this talk is to investigate the case where operators A and B are either unobserved
or difficult to handle numerically. We propose an online version of the forward-backward algorithm where at each iteration, A and B are replaced
with one realization of some random maximal monotone operators whose expectations (in the Aumann sense) coincide with A and B respectively.
Under the assumption of a decreasing step size, we prove that the iterates "shadow" the behavior of a continuous-time differential inclusion
and converge almost surely to a zero of A+B provided some conditions. Applications to constrained convex optimization are considered.
[INMA] 2015-11-10 (14:00) : Matrix geometric means
At Euler building (A002)
Speaker :
Bruno Iannazzo (Università di Perugia)
Abstract : A pleasant activity in Matrix Analysis is to try and generalize concepts from scalars to matrices. In this perspective, it is understood the quest for the definition of a geometric mean of Hermitian positive definite matrices. After many imperfect attempts, the "right" definition has been unearthed using a differential geometry argument. The interest in the matrix geometric mean is not just theoretical, since this matrix function has great power in averaging and interpolating positive definite matrices and hence is well suited for modeling. Thus, there is the need of good algorithms for computing it. We will tell the long journey to the definition of matrix geometric mean, briefly describe some applications and focus on the numerical methods for computing these means. Finally, we will discuss some lines of research in this topic.
[INMA] 2015-11-03 (14:00) : Presentations by three PhD students
At Euler building (A002)
Speaker :
Massart, Estelle
,
Benjamin Vincent (UCLouvain)
,
and
Gutierrez Gomez, Efrain Leonardo
Abstract : Three PhD students will explain their topics. Benjamin Vincent: "Inferential command of distributed thermodynamics systems. Application to the Tokamak." Leonardo Gutierrez: "Learning networks". Estelle Massart: "Data fitting on manifolds"
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