All Years Seminars
[INMA] 2019-10-15 (14:00) : Modelling and Analysis of Opinion Dynamics on Social Networks
At Euler building (room A.002)
Speaker :
Mengbin Ye (University of Groningen, Netherlands)
Abstract :
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.
[INMA] 2019-10-08 (14:00) : Two 20-minute talks
At Euler building (room A.002)
Section 1:Proximal Method with Contractions for Smooth Convex Optimization
Speaker :
Doikov, Nikita
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.
Section 2:Greedy Quasi-Newton Method with Explicit Superlinear Convergence
Speaker :
Anton Rodomanov (CISPA, Germany)
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.
[INMA] 2019-10-01 (14:00) : Two 20-minute talks
At Euler building (room A.002)
Section 1:Alternating minimization algorithm for graph regularized tensor completion
Speaker :
Guan, Yu
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.
Section 2:Optimization Problems with Orthogonality Constraints -- from Feasible to Infeasible
Speaker :
Gao, Bin
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.
[INMA] 2019-09-24 (14:00) : Global Stabilization of the Navier-Stokes Equations Around an Unstable Steady State
At Euler building (room A.002)
Speaker :
Abdou Sene (LANI - Laboratoire d'Analyse Numérique et Informatique [Sénégal])
Abstract :
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.
[INMA] 2019-09-17 (14:00) : Discrete Mumford-Shah model: from image restoration to graph analysis
At Euler building (room A.002)
Speaker :
Pustelnik, Nelly
Abstract :
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.
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