The Departement of Mathematical Engineering organizes a series of seminars. The seminars are usually held on Tuesday from 2:00pm to 3:00pm in the Euler lecture room, Building EULER, av. Georges Lemaître 4-6, Louvain-la-Neuve (Parking 13). Be mindful that exceptions may occur; see the talk annoucements.
If you wish to receive the seminar announcements by email, please send an email to Etienne Huens.
Master students can take this seminar for credit in either of the two semesters; see LINMA2120 for more information.
Seminars to come
|09/06/2020 (14:00) [Lieu : MS Teams]|
Yurii Nesterov (UCLouvain)
Online prediction of COVID19 dynamics. Belgian case study
In this talk, we present a new axiomatic model of epidemic development, which is consistent with the very special features of COVID19. This is a discrete-time switching linear model for predicting the dynamics of total number of infected persons and concentration of the asymptomatic virus holders in population. A small number of its parameters can be tuned using the available real-time dynamic data on virus propagation. Therefore, this model provides us also with online prediction of the future. As an application example, we present the conclusions of this model for epidemic of COVID19 in Belgium in 2020. During several months, our predictions were exact, typically, within the accuracy of 0.5%.
|26/05/2020 (14:00) [Lieu : MS Teams]|
Sébastien Colla (UCLouvain)
A 20-minute talk given by a student (2/2)
Title: Derivative Free Optimization : Directional direct search methods
Abstract: Derivative free optimization (DFO) is the study of « zero order methods » that use no derivatives to find (or approach) the optimum of a problem. Nowadays there are many optimization problems for which the derivative computation is very expensive or noisy or even impossible. Without the use of the derivative we cannot expect the same performance as the classical first-order methods, but it is still possible to have methods that are guaranteed to converge to some stationary point. This is the case of the directional direct-search methods that poll multiples points in different well-chosen direction at each iteration and choose as next iterate the one that (best) decreases the objective. A basic example of this is the coordinate search method. The seminar will focus on this set of direct-search derivative free methods and their convergence results.
|19/05/2020 (13:30) [Lieu : MS Teams]|
Mattéo Couplet and Julien Calbert (UCLouvain)
Two 20-minute talks given by the students (1/2)
Please note the unusual time of this event (starting at 13:30).
Speaker: Mattéo Couplet
Title: Random Projections, Compressive Sensing and Compressive Classification
Abstract: About a decade ago, groundbreaking papers revealed the possibility of faithfully recovering high-dimensional signals from some incomplete information about them. They gave rise to the field of compressive sensing, which is now in a mature state and whose foundations rely on an elegant mathematical theory. This talk will start with an overview of the field. Then, the compressive classification task will be addressed, for which it can be shown that even fewer compressive measurements are required than for signal reconstruction, using ideas from high-dimensional convex geometry.
Speaker: Julien Calbert
Title: Proximal methods
Abstract: In this talk, we will discuss a particular class of optimization algorithms: proximal algorithms. These algorithms are well suited to solve convex, non-smooth, constrained and large-scale optimization problems. They are based on the successive resolution of a convex optimization problem called proximal operator. These methods are of great interest because they work under general conditions, they can be fast if a closed form can be derived for the proximal operator and under certain conditions they can be solved in a distributed way. In addition, proximal methods can be seen as an additional level of abstraction to the classical optimization methods. They form a theoretical framework for demonstrating simultaneously the convergence of several optimization methods such as the gradient method or the projected gradient method. Finally, we will see several applications in the field of signal processing.
|12/05/2020 (14:00) [Lieu : MS Teams]|
Philippe Lefèvre (UCLouvain)
Prediction and uncertainty in the control of visual tracking
Vision plays a key role in behaviour. In humans, visual acuity is non-homogeneous across the visual field and is characterized by a foveal zone of very high resolution. Therefore, for human observers, the quality of visual inputs is heavily influenced by their ability to detect and fixate parts of the visual scene that are of particular interest. When everything is stationary if the environment, this is performed with saccades that are fast orienting eye movements allowing to scan the visual scene. However, in a dynamic environments, objects can move with respect to the observer, requiring to track moving objects with smooth pursuit eye movements. Saccades and smooth pursuit eye movements are two different modes of oculomotor control. However, behavioural and neurophysiological data demonstrated that both types of eye movements work in synergy for visual tracking. This suggests that saccades and pursuit are two outcomes of a single sensorimotor process that aims at orienting the visual axis. More recently, it has been hypothesized that oculomotor behaviors integrate sensory (visual) and prior information to overcome sensory-motor delays and noise. After much debate about this process, reliability-based integration has recently been proposed and several models of smooth pursuit now include recurrent Bayesian integration or Kalman filtering. In this talk, I will present some recent experimental and modeling work demonstrating the key role played by prediction and uncertainty in the synergy between saccades and smooth pursuit in the control of visual tracking.
|05/05/2020 (14:00) [Lieu : MS Teams]|
Tim Marrinan (COLORAMAP Group, UMons)
Identifiability and Detection of Multiset Correlation Structure
Relationships between random vectors with deterministic but unknown linear mixing are commonly assessed via canonical correlations. Detecting this correlation structure allows us to infer unseen associations between the underlying variables. For example, this type of analysis has been used to identify conditions that lead to a rise in sea surface temperature and to localize regions of brain activity used for visual recognition tasks. For pairs of random vectors, general conditions have been discovered under which the correlation structure is identifiable, but for collections of more than two random vectors such general conditions remain evasive. In this lecture we describe conditions under which a subset of multiset correlation structures can be identified, and demonstrate how the correlation structures can be detected from the augmented coherence matrix of the data.
|28/04/2020 (14:00) [Lieu : MS Teams]|
Julien Hendrickx (UCLouvain)
Challenges in Open Multi-Agent Systems Subject to Arrivals and Departures
Scalability and robustness to agent losses are often cited as advantages of multi-agent systems, but almost all theoretical results apply to system with fixed compositions. We consider open systems, that agents continuously leave and join during the process considered. We discuss the general challenges to analyze and design algorithms for such systems. Challenges in the analysis come from the fact that each arrival or departure implies a discontinuity and a change of the system state dimension. Moreover, these repeated events forbid any asymptotic convergence. On the design side, arrivals perturb the system and may also modify the algorithms objective. Departures result in information loss, or conversely, in a persistent influence of information that is no longer relevant. Moreover, correction mechanisms designed to cope with a small number of arrivals or departures may fail or even have a counterproductive and destabilizing effect, when these events keep taking place. We focus in particular on averaging, decentralized estimation, computation of the maximum value and decentralized optimization. We also present some fundamental performance limitations in open systems.
|21/04/2020 (14:00) [Lieu : MS Teams]|
Christophe De Vleeschouwer (UCLouvain)
Deep Learning in Computer Vision
Deep learning and more specifically Convolutional Neural Networks (CNNs) are now predominant in computer vision. In this seminar, we survey a variety of image processing problems and present how they are formulated in terms of CNNs optimization, using image-wise or pixel-wise predictions. We then introduce some of the practical issues encountered when training and deploying neural networks in real-life, which reveals that a major shortcoming of neural networks lies in the poor understanding we have about their inner processes and generalization capabilities. Since a solid mathematical framework is still lacking to explain neural networks performance, we summarize a few recent experimental results revealing the tight connection between network pruning and generalization. Those results suggest to look for an explanation in the way neurons split data in diverse and representative binary classes.
|03/03/2020 (15:00) [Lieu : Euler building (room A.002)] |
Special event: visit of intoPIX
The students from the Seminar in Applied Mathematics (LINMA2120) organize a visit intoPIX, an LLN-based world-class company specialized in image processing, video compression and security technologies.
Registration is free but mandatory (number of places limited; the registraiton form has been sent by email)
The schedule is as follows:
15:00: meeting at the entrance of the Euler building for group departure (carpool)
15:30: start of the visit
16:30 (approx.): end of the visit and drink
|03/03/2020 (14:00) [Lieu : Euler building (room A.002)]|
Alexandre Mauroy (UNamur, Belgium)
Koopman operator-based identification of nonlinear ODEs and PDEs
The Koopman operator provides a linear description of nonlinear systems. In this talk, we will exploit this description in the context of nonlinear identification and parameter estimation. Since the generator of the semigroup of Koopman operators is directly connected to the underlying dynamics, we will exploit the key idea that identifying the linear generator is equivalent to identifying the nonlinear dynamics. Using this systematic approach, we will report on two dual linear techniques. These techniques will be illustrated with several examples and complemented with convergence properties derived from the theory of strongly continuous linear semigroups. Finally, the proposed identification framework will be extended to nonlinear PDEs by considering Koopman operator semigroups acting on a space of nonlinear functionals.
|25/02/2020 (14:00) [Lieu : Euler building (room A.002)]|
Alexander Stollenwerk (TU Berlin, Germany)
Binarizing Johnson-Lindenstrauss transforms
In many problems from data science, the encountered data is massive and encoded by high-dimensional vectors. For applications it is therefore appealing to first reduce its dimensionality before performing computations. If enough geometric information between data vectors is preserved, then the problem can be solved approximately using the embedded data. In this talk, we will focus on the problem of encoding a set of high-dimensional vectors into a small number of bits, while approximately preserving their pairwise Euclidean distances. By binarizing fast Johnson-Lindenstrauss transforms, we will see that this can be achieved efficiently, even for infinite data sets of low-complexity. The talk is based on joint work with Sjoerd Dirksen.
|19/02/2020 (14:00) [Lieu : Euler building (room A.207)]|
Miel Sharf (Technion, Israel)
Model-Free Practical Cooperative Control Using Passivity and Network Optimization
Please note the unusual location and day of this talk.
In recent times, networked control systems have become an important field of research, as multi-agent and large-scale networks have become common, and the system-of-systems design philosophy has become the state-of-the-art. The ever-growing complexity of systems makes the process of obtaining a reliable mathematical model arduous and time-consuming, especially for networked systems which include many different agents corresponding to many different models. Coincidentally, technological advancements introduced more efficient ways to gather, store, and analyze data. This motivates the idea of data-driven controller design, in which data is used to solve control problems, either by building an approximate model for the system, or by learning a control policy directly.
In this talk, we'll consider a problem in which the relative output between the (nonlinear) agents must converge -close to prescribed values (e.g., consensus or formation control). Our approach relies on a connection between passivity theory and network optimization, as well as high-gain control. We use network optimization to show not only that there exists a gain attaining the desired control goal, but also prescribe a data-driven method of estimating it. We further present another data-driven solution using iterative sampling schemes. We will also discuss how to verify the required passivity assumptions and illustrate the developed methods in a case study.
The talk is based on joint work with Anne Romer, Daniel Zelazo and Frank Allgöwer.
|18/02/2020 (14:00) [Lieu : Euler building (room A.002)]|
Adrien Taylor (INRIA, France)
Computer-aided worst-case analyses and design of first-order optimization methods
The goal of this presentation, is to provide a high-level overview of recent computer-assisted approaches for analyzing and designing first-order optimization methods (mostly for convex optimization). In other words, we want to illustrate how to use computer algebra software (symbolic computations) and/or numerical tools (semidefinite programming solvers) for analyzing optimization schemes. The presentation will be example-based, as the main ingredients necessary for understanding the methodologies are already present in basic examples such as the vanilla gradient method. For convincing the audience, we will provide other examples that include novel analyses of the Douglas-Rachford splitting, and a variant of the celebrated conjugate gradient method.
|11/02/2020 (14:00) [Lieu : Euler building (room A.002)]|
Sasa V. Rakovic (Beijing Institute of Technology)
Minkowski, Lyapunov, and Bellman: Inequalities and Equations for Stability and Optimal Control
The algebraic Lyapunov and Bellman equations, and inequalities, are cornerstone objects in linear systems theory. These equations, and inequalities, are concerned with convex quadratic functions verifying stability in case of Lyapunov equation and providing optimality in case of Bellman equation. Rather peculiarly, very little had been known about Lyapunov and Bellman equations, and inequalities, within space of Minkowski functions of nonempty convex compact subsets containing the origin in their interior prior to my work in the area. Key results of my related research on these fundamental problems have provided characterization of solutions to both Lyapunov and Bellman equations within space of Minkowski functions, referred to as the Minkowski Lyapunov and Minkowski Bellman equations. The talk outlines key results underpinning these two fundamental equations and related inequalities, and draws parallel to classical results on algebraic Lyapunov and Bellman equations and inequalities.
|04/02/2020 (14:00) [Lieu : Euler building (room A.002)]|
Antoine Legat, Ousmane Diao, and Julien Dewez (UCLouvain)
Three 15-minute talks
Speaker: Antoine Legat
Title: Local dynamics identification via a graph-theoretical approach
Abstract: In this talk we propose a novel approach to network identification: the recovery of the local dynamics from the global input-output behavior and the network structure. First, we express identifiability conditions on the rank of transfer matrices, which can be computed by routing vertex disjoint paths in the network. We then address the unstudied case of partial measurement and excitation, and derive a linearization which yields promising conditions for the identifiability of the whole network, backed up by our implementation.
Speaker: Ousmane Diao
Title: Mathematical modeling of malaria transmission taking into account the influence of current prevention and treatment
Abstract: Malaria is a parasitic infection transmitted by a mosquito (female Anophele) which is very deadly for humans. Many strategies are provided from the Senegal s National Malaria Control Program of to reduce morbidity and mortality. We have insecticide-treated bed-nets (ITNs), Vaccines, L'Artemisinin-based combination therapy (ACT) and indoor residual spraying (IRS) etc For it, mathematical modelling may play an important role in operational and optimizing this strategies on control. So we want to develop compartments mathematical model of malaria transmission to show the effects of prevention and treatment.
Speaker: Julien Dewez
Title: Lower bounds for the nonnegative rank
Abstract: Nonnegative matrix factorization (NMF) consists in finding two nonnegative matrices whose product is equal to/approximates a nonnegative data matrix. It has many interesting applications in data analysis when the observed data is nonnegative by nature, e.g., in text mining, in hyperspectral unmixing, and many more. Computing the minimum dimension of such a factorization, called the nonnegative rank, is NP-hard in general. However, it also has interesting applications, e.g., in combinatorial optimization, in statistics, etc. In this talk, we introduce new lower bounds on the nonnegative rank based on properties of some geometric representations of the matrix.
|17/12/2019 (14:00) [Lieu : Euler building (room A.002)]|
Florentin Goyens (Alan Turing Institute and University of Oxford, UK)
Nonlinear matrix recovery
In this talk we investigate the recovery of a partially observed high-rank matrix whose columns obey a nonlinear structure. The structures we cover include points grouped as clusters or belonging to an algebraic variety, such as a union of subspaces. Using a mapping to a space of features, we reduce the problem to a constrained non-convex optimization formulation, which we solve using Riemannian optimization methods. We also show how the same tools allow to align point clouds that belong to the same algebraic variety (point set registration).
|10/12/2019 (14:00) [Lieu : Euler building (room A.002)]|
Pascal Barbara (ENS Lyon, France)
How scale-free texture segmentation turns out to be a strongly convex optimization problem?
Texture segmentation still constitutes an ongoing challenge, especially when processing large-size images. The aim of this work is twofold. First, we provide a variational model for simultaneously extracting and regularizing local texture features, such as local regularity and local variance. For this purpose, a scale-free wavelet-based model, penalised by a Total Variation regularizer, is embedded into a convex optimisation framework. Second, we investigate convergence acceleration strategies, relying on strong-convexity of the objective function, in order to deal with computational cost induced by the minimization. Finally, we illustrate the developed procedures on real-world images of multiphasic flows.
|03/12/2019 (14:00) [Lieu : Euler building (room A.002)]|
Tsiaflakis Paschalis (Nokia Bell Labs, Antwerp)
Optimization for ultrabroadband internet access
Broadband internet access is an essential part in modern life society. Offering universal, cheap and ultrabroadband internet connectivity is a top priority within the European Digital Agenda. The Nokia Bell Labs Fixed Networks Team located in Antwerp is recognized for pioneering and contributing to breakthroughs in wireline broadband internet access technologies. These technologies enable data communication at gigabit speeds between residential customers and the fiber backbone, and are characterized by optimization-intensive physical-layer designs. This seminar will explain a number of optimization problems that are considered in practice to innovate communication technologies. The main aim of this seminar is to show that the application of optimization theory is very relevant for industry.
|26/11/2019 (14:00) [Lieu : Euler building (room A.002)]|
Rolando Mosquera and Antoine Falaize (LaSIE, Université de la Rochelle, France )
Some geometric and machine learning methods for model order reduction
Geometric methods have proved to be effective for data mining (simulations, measurements) in the context of nonlinear model order reduction problems in mechanics (e.g. nonlinear methods for dimensionality reduction such as Local Principal Component Analysis, LPCA or Locally Linear Embedding, LLE). In addition, deep learning methods by so-called neural network (NN) architectures proved to be effective for a class of problems involving data classification, detection and compression.
We first present a set of geometric tools for the interpolation of reduced bases obtained by orthogonal decomposition (POD) of simulation results. More precisely, by exploiting the intrinsic geometry of the sub- spaces engendered by the POD bases, we give the construction of different interpolators on the Grassmann manifold.
Then, we use the architecture of neural networks to extract geometric informations about the data manifold. More precisely, a metric on the manifold can be found from the representations of coordinates learned by the network. Conversely, classical architectures of neural networks can be informed by the geometry of the data to build optimizers that respect the local geometry. These approaches are illustrated on model order reduction problems in mechanics.
|19/11/2019 (14:00) [Lieu : Euler building (room A.002)]|
Tran Nhan Tam Quyen (Institute for Numerical and Applied Mathematics, University of Goettingen, Germany.)
Parameter identification in elliptic PDEs from boundary data: finite element method with total variation regularization
In this presentation we would like to present the problem of identifying the conductivity and the source term in elliptic PDEs from several sets of boundary data. The finite element method with total variation regularization technique is applied to tackle the ill-posed identification problem. We analyze the stability of the proposed approach and the convergence of the finite element regularization approximations to the sought parameters, which confirm that the parameters distributed inside the physical domain can be reconstructed from a finite number of observations on the boundary.
|12/11/2019 (14:00) [Lieu : Euler building (room A.002)]|
Necmiye Ozay (Univ. Michigan, USA)
Control synthesis for large collections of dynamical systems with counting constraints
Can we control a swarm of systems and give guarantees on their collective behavior? In this talk I will discuss an instance of this problem: given a large almost homogeneous collection of dynamical systems and a novel class of safety constraints, called counting constraints, how to synthesize a controller that guarantees the satisfaction of these constraints. Counting constraints impose restrictions on the number of systems that are in a particular mode or in a given region of the state-space over time. I will present an approach for synthesizing correct-by-construction controllers to enforce such constraints. Our approach exploits the structure of the problem, the permutation invariance of dynamics due to homogeneity and the permutation invariance of counting constraints, to achieve massive scalability. I will discuss several potential applications of this approach and illustrate it on the problem of coordinating a large collection of thermostatically controlled loads while ensuring a bound on the number of loads that are extracting power from the electricity grid at any given time.
|05/11/2019 (14:00) [Lieu : Euler building (room A.002)]|
Guillaume Van Dessel and Brieuc Pinon (UCLouvain)
Two 20-minute talks
Speaker: Guillaume Van Dessel
Title: Convex optimization using tunable first-order inexact oracles (TFOIO)
Abstract: In this talk will be introduced/ motivated the concept of tunable first-order inexact oracle (TFOIO) in convex optimization. More specifically: It will be first discussed convergence results for smooth-convex optimization methods such as (P)GD and FGD taking into account for inexactness both in the information used (tunable first-order inexact oracle built upon surrogates for the objective function and its (sub)gradient) and the accuracy on the update steps. Then it will be shown how and when it is possible to derive, based on a cost (either computational or economical) associated with oracle calls, optimal schedules for the above methods. Worst-case cost gains will be presented for a proper set of chosen experiments. Finally, if the time allows it, practical examples using a personal toolbox will be displayed in live to confirm the empirical behavior of the cited methods under the use of inexact information.
Speaker: Brieuc Pinon
Title: New developments in Machine Learning: a Kolmogorov Complexity approach
Abstract: We first identify some intrinsic limitations in currently used learning algorithms in Machine Learning. These algorithms lack of learning automatization and expressiveness in order to efficiently exploit some structures in some complex tasks. A solution can be found within the Kolmogorov Complexity framework, "perfect" learning that exploits all computable patterns in the data exists. However, it is non-computable. We point to potential practical solutions for this problem, and theoretical questions that we investigate. An understanding of introductory notions in Machine Learning and Theoretical Computer Science is advised.
|29/10/2019 (14:00) [Lieu : Euler building (room A.002)]|
Gianmarco Ducci (UCLouvain (IMMC))
Gait parametrization and limit cycle stability of flapping bird flight
The biomechanics of birds is of crucial interest for modern engineering applications. Indeed, flapping birds display the ability of maintaining a stable flight in a continuously perturbed environment, while executing complex maneuvers. We developed a method identifying trimmed flight conditions for flapping wings. These particular conditions correspond to limit cycles in the state space domain, with the same period as the flapping input. Our method is based on a multiple-shooting algorithm that can simultaneously identify unknown limit cycles of the longitudinal equations of bird s motion, and assess its stability relying on Floquet theory. This framework further employs a lifting line aerodynamic model developed in the group of fluid mechanics at UCLouvain. Consequently, sensitivity analysis of gait configurations as a function of the wing kinematic parameters can be conducted. Results suggest that birds should continuously rely on feedback control scheme to achieve steady-state flapping flight, and possible solutions to achieve such flight stabilization are discussed.
|15/10/2019 (14:00) [Lieu : Euler building (room A.002)]|
Mengbin Ye (University of Groningen, Netherlands)
Modelling and Analysis of Opinion Dynamics on Social Networks
Social network analysis is a rich and exciting area of interdisciplinary research that has been tackled by many different scientific communities. Opinion dynamics is a popular topic which uses mathematical models to describe how opinions change as individuals interact over a network. Two recent developments are presented from the perspective of a systems and control engineer, giving some insight into how individual-level processes combine with network-level interactions to determine the evolution, including limiting values, of opinions in the network. In the first part, a novel model is proposed to describe how an individual s private and expressed opinions (which are not the same in general) evolve under pressure to conform to the group norm. We establish sufficient conditions for a discrepancy to arise between an individual s private and expressed opinions on general networks. We then use the model to explore Asch's conformity experiments and the phenomenon of pluralistic ignorance. In the second part, we consider a model that captures a group of individuals simultaneously discussing logically interdependent topics. We show that when heterogeneity exists in the way individuals view the logical interdependencies, disagreement can arise because of the logical interdependence structure, even though all individuals are trying to reach a consensus of opinions.
|08/10/2019 (14:00) [Lieu : Euler building (room A.002)]|
Nikita Doikov and Anton Rodomanov (UCLouvain)
Two 20-minute talks
Speaker: Nikita Doikov
Title: Proximal Method with Contractions for Smooth Convex Optimization
Abstract: In this talk we study a construction of proximal accelerated methods for smooth convex optimization. At every step the method minimizes a sum of contracted objective and a regularizer in a form of Bregman divergence, by some auxiliary subroutine. We present complexity analysis for a general scheme. In the case when Tensor Method is used as internal method, we show accelerated rate of convergence with additional logarithmic factor as a cost for solving the subproblem.
Speaker: Anton Rodomanov
Title: Greedy Quasi-Newton Method with Explicit Superlinear Convergence
Abstract: We propose a new quasi-Newton method for unconstrained minimization of smooth functions. Our method is based on the famous BFGS scheme but it uses a greedily selected coordinate vector for updating the Hessian approximation instead of the previous search direction. We prove that the proposed method has local superlinear convergence and establish a precise bound for its rate. To our knowledge, this result is the first explicit non-asymptotic rate of superlinear convergence for quasi-Newton methods.
|01/10/2019 (14:00) [Lieu : Euler building (room A.002)]|
Yu Guan and Bin Gao (UCLouvain)
Two 20-minute talks
Speaker: Yu Guan
Title: Alternating minimization algorithm for graph regularized tensor completion
Abstract: In this talk, we consider low-rank tensor completion problem which aims to exactly recover a low-rank tensor from an incomplete observation. It plays an important role in many applications such as signal processing, computer vision, machine learning, and neuroscience. A widely used convex relaxation of low-rank tensor completion problem is to minimize the sum of the nuclear norm of its unfolding matrices. We build our low-rank completion model based on the CANDECOMP/PARAFAC decomposition approach. In order to improve the recovery quality, the graph information such as correlations between the column/row entities from the side matrices are exploited. In this paper, we propose efficient alternating minimization algorithms combined with conjugate gradient method or alternating direction method of multiplier method dealing with the subproblems. Furthermore, based on the Kurdyka- ojasiewicz property, we show that the sequence generated by the alternating minimization globally converges to a critical point of the objective function since our model is a Kurdyka- ojasiewicz function. Moreover, the complexity and convergence rate of proposed algorithms are also derived. In addition, the regularizer terms in the model could be reformulated as a generalized weighted nuclear norm. As a result, the statistical consistency is guaranteed for our completion problem. Extensive numerical experiments including synthetic data, real data indicate the proposed algorithms are effective.
Speaker: Bin Gao
Title: Optimization Problems with Orthogonality Constraints -- from Feasible to Infeasible
Abstract: To construct a parallel approach for solving optimization problems with orthogonality constraints is usually regarded as an extremely difficult mission, due to the low scalability of the orthogonalization procedure. However, such demand is particularly huge in some application domains such as material computation. In this talk, we introduce several efficient algorithms including feasible and infeasible methods. Such methods have much lower computational complexity and can also benefit from parallel computing since they are full of BLAS3 operations. In the infeasible algorithm based on a modified augmented Lagrange method, the orthogonalization procedure is only invoked once as the last step. Consequently, the main parts of the proposed algorithms can be parallelized naturally. We establish global subsequence convergence results for our proposed algorithms. Worst-case complexity and local convergence rate are also studied under some mild assumptions. Numerical experiments, including tests under parallel environment, illustrate that our new algorithms attain good performances and high scalability in solving discretized Kohn-Sham total energy minimization problems.
|24/09/2019 (14:00) [Lieu : Euler building (room A.002)]|
Abdou Sene (LANI - Laboratoire d'Analyse Numérique et Informatique [Sénégal])
Global Stabilization of the Navier-Stokes Equations Around an Unstable Steady State
We present a mixed (Dirichlet-Neumann) boundary feedback controller for stabilizing the Navier-Stokes equations around a prescribed steady state, in a bounded domain. The Neumann part of the boundary controller is designed to be zero when the inflow vanishes, and to have the magnitude of the kinetic energy. An appropriate choice of the controllers allows to prove exponential decrease of the perturbation in L2, without blowup. In addition, we prove, on the one hand, that the exponential convergence towards zero holds in H1, on the other hand, that the weak solution is unique when the computational domain is two-dimensional. The procedure we adopt is mainly based on the Galerkin discretization method, and the use of compacity results. Indeed, the stabilization is achieved first for the finite dimensional system, then we pass to the limit by exploiting compactness theory.
|17/09/2019 (14:00) [Lieu : Euler building (room A.002)]|
Nelly Pustelnik (ENS Lyon, France)
Discrete Mumford-Shah model: from image restoration to graph analysis
The Mumford Shah model is a standard model in image segmentation and many approximations have been proposed in order to approximate it. The major interest of this functional is to be able to perform jointly image restoration and contour detection. In this work, we propose a general formulation of the discrete counterpart of the Mumford Shah functional. We derive a new proximal alternated minimization scheme, allowing to deal with the non-convex objective function, with proven convergence and numerical robustness to the initialization. The good behavior of the proposed strategy is evaluated and compared to state-of-the art approaches in image restoration and extended to graph analysis.
|06/09/2019 (14:00) [Lieu : Euler building (room A.002)]|
Martin Gueuning (UNamur-UCLouvain, Belgium)
Spreading and diffusion on temporal networks
Network theory provides a framework to model interacting systems from many different fields. The recent increase in the availability of empirical data has allowed to take into account more realistic characteristics of the networks. In particular, the details of the timing of the interactions have highlighted the non-Markovian nature of the agents in many systems. In this work, we investigate stochastic processes on temporal networks. First, we study the impact of non-Markovian activities on Random Walks. We show that memory in the trajectory of the random walker naturally emerges due to bursty behaviours and the presence of short cycles. Second, we investigate spreading strategies on temporal networks. In particular, we show that the temporal sequence of a cascade of retweets may provide an insight about the way it spread on the network and how to exploit it to provide a list of users to target simultaneously, in order to maximize the final share of a message.
|27/08/2019 (15:00) [Lieu : Euler building (room A.002)]|
Debdipta Goswami (University of Maryland)
Koopman Based Control: Bilinearization, Controllability and Optimal Control of Control-Affine Nonlinear Systems
Note the unusual time of this talk (15:00).
Nonlinear systems are ubiquitous in real world applications, but the control design for them is not an easy task. Hence, methods are sought to transform a control-affine nonlinear system into linear or bilinear forms to alleviate the problem of nonlinear controllability and control design. While there are linearization techniques like Carleman linearization for embedding a finite-dimensional nonlinear system into an infinite-dimensional space, they depend on the analytic property of the vector fields and work only on polynomial space. The Koopman-based approach described here utilizes the Koopman Canonical Transform (KCT) to transform the dynamics and ensures bilinearity from the projection of the Koopman operator associated with the control vector fields on the eigenspace of the drift Koopman operator. The sufficient conditions for exact bilinearization are derived. Even if the conditions are not fully met, the approximate bilinearization can also be posed as an optimization problem. The resulting bilinear system is then subjected to controllability analysis using the Myhill semigroup method and Lie algebraic structures. Using the same Myhill semigroup structure, we also seek to prove the existence of an energy-only optimal control.