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

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).

Previous seminars

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.