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Cena NumPi
by Leonardo Robol 30 Jun '21

30 Jun '21

Cari tutti, come gli anni scorsi (ed in particolare quelli non-pandemici), vorremmo provare ad organizzare una cena di "fine seminari"; più che altro sarebbe una scusa per vedersi, a maggior ragione quest'anno dove non ci siamo (quasi) mai incontrati di persona. Ho predisposto un Doodle dove potete segnare la vostra disponibilità, se intendete partecipare: https://doodle.com/poll/z2xw2k6u5zzfybn3 Siete tutti benvenuti (dagli ordinari ai dottorandi, ma anche simpatizzanti, ecc.). Vi chiederei solo di segnare la vostra presenza quanto prima così che riusciamo ad organizzarci per bene. Il luogo non è stato ancora scelto, ma proposte sono sempre bene accette; probabilmente dovremo scegliere anche in funzione del numero di partecipanti. A presto! -- Leonardo Robol.

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Reminder: Seminar today (Stefano Cipolla)
by Fabio Durastante 18 Jun '21

18 Jun '21

Speaker: Stefano Cipolla Affiliation: University of Edinburgh Time: Friday, 18/06/2021, 16:00 Title: Random multi-block ADMM: an ALM based view for the QP case Because of its wide versatility and applicability in multiple fields, the n-block alternating direction method of multipliers (ADMM) for solving nonseparable convex minimization problems, has recently attracted the attention of many researchers [1, 2, 4]. When the n-block ADMM is used for the minimization of quadratic functions, it consists in a cyclic update of the primal variables xi for i = 1,...,n in the Gauss-Seidel fashion and a dual ascent type update of the dual variable μ. Despite the fact the connections between ADMM and Gauss-Seidel are quite well known, to the best of our knowledge, an analysis from the purely numerical linear algebra point of view is lacking in literature. Aim of this talk is to present a series of very recent results obtained on this topic which shed further light on basic issues as convergence and efficiency [3]. [1] Chen, C., Li, M., Liu, X., Ye, Y. (2019). Extended ADMM and BCD for nonseparable convex minimization models with quadratic coupling terms: convergence analysis and insights. Mathematical Programming, 173(1-2), 37-77. [2] Chen, C., He, B., Ye, Y., Yuan, X. (2016). The direct extension of ADMM for multi-block convex minimization problems is not necessarily convergent. Mathematical Programming, 155(1-2), 57-79. [3] Cipolla, S., Gondzio, J (2020). ADMM and inexact ALM: the QP case. arXiv 2012.09230. [4] Sun, R., Luo, Z. Q., Ye, Y. (2020). On the efficiency of random permutation for ADMM and coordinate descent. Mathematics of Operations Research, 45(1), 233-271. https://www.dm.unipi.it/webnew/it/seminari/random-multi-block-admm-alm-base… <https://www.dm.unipi.it/webnew/it/seminari/random-multi-block-admm-alm-base…> Meeting link: https://hausdorff.dm.unipi.it/b/leo-xik-xu4 <https://hausdorff.dm.unipi.it/b/leo-xik-xu4>

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Colloquium on 16/06 at 5pm (Volker Mehrmann)
by Paola Boito 16 Jun '21

16 Jun '21

Dear all, An online colloquium of the Department of Mathematics at UniPi is planned on June 16 at 17:00. You are all welcome! The speaker is Volker Mehrmann (TU Berlin). Title: Energy based modeling, simulation, and control. Mathematical theory and algorithms for the solution of real world problems. Abstract: Energy based modeling via port-Hamiltonian systems is a relatively new paradigm in all areas of science and engineering. These systems have wonderful mathematical properties, concerning their analytic, geometric and algebraic properties, but also with respect to their use in numerical algorithms for space-time discretization, model reduction and control. We will introduce the model class and their mathematical properties and we illustrate their usefulness with several real world applications. Google Meet link: https://meet.google.com/qii-tcks-rrr

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Seminar on 18/06 (Stefano Cipolla)
by Leonardo Robol 14 Jun '21

14 Jun '21

Speaker: Stefano Cipolla Affiliation: University of Edinburgh Time: Friday, 18/06/2021, 16:00 Title: Random multi-block ADMM: an ALM based view for the QP case Because of its wide versatility and applicability in multiple fields, the n-block alternating direction method of multipliers (ADMM) for solving nonseparable convex minimization problems, has recently attracted the attention of many researchers [1, 2, 4]. When the n-block ADMM is used for the minimization of quadratic functions, it consists in a cyclic update of the primal variables xi for i = 1,...,n in the Gauss-Seidel fashion and a dual ascent type update of the dual variable μ. Despite the fact the connections between ADMM and Gauss-Seidel are quite well known, to the best of our knowledge, an analysis from the purely numerical linear algebra point of view is lacking in literature. Aim of this talk is to present a series of very recent results obtained on this topic which shed further light on basic issues as convergence and efficiency [3]. [1] Chen, C., Li, M., Liu, X., Ye, Y. (2019). Extended ADMM and BCD for nonseparable convex minimization models with quadratic coupling terms: convergence analysis and insights. Mathematical Programming, 173(1-2), 37-77. [2] Chen, C., He, B., Ye, Y., Yuan, X. (2016). The direct extension of ADMM for multi-block convex minimization problems is not necessarily convergent. Mathematical Programming, 155(1-2), 57-79. [3] Cipolla, S., Gondzio, J (2020). ADMM and inexact ALM: the QP case. arXiv 2012.09230. [4] Sun, R., Luo, Z. Q., Ye, Y. (2020). On the efficiency of random permutation for ADMM and coordinate descent. Mathematics of Operations Research, 45(1), 233-271. https://www.dm.unipi.it/webnew/it/seminari/random-multi-block-admm-alm-base… Meeting link: https://hausdorff.dm.unipi.it/b/leo-xik-xu4

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Math Colloquium - Lars Ruthotto - June 17 at 17:00
by Francesco Tudisco 14 Jun '21

14 Jun '21

Dear all, the next GSSI Math Colloquium will be held on *Thursday June 17 at 5pm* (please note **the time is *5pm* instead of the usual 3pm**). The speaker is Lars Ruthotto, with a lecture connecting numerical methods for differential equations and deep learning architectures. More details below. Lars Ruthotto is Associate Professor of Mathematics and Computer Science at Emory University (Atlanta, USA). To attend the talk please use to the following Zoom link: https://us02web.zoom.us/j/85179454721?pwd=TjA0V2M3L3lVTk1NNEdVcGpQcXlTdz09 Please feel free to distribute this announcement as you see fit. Looking forward to seeing you all on Thursday! Paolo Antonelli, Stefano Marchesani, Francesco Tudisco and Francesco Viola --------------------- Title: Numerical Methods for Deep Learning motivated by Partial Differential Equations Abstract: Understanding the world through data and computation has always formed the core of scientific discovery. Amid many different approaches, two common paradigms have emerged. On the one hand, primarily data-driven approaches—such as deep neural networks—have proven extremely successful in recent years. Their success is based mainly on their ability to approximate complicated functions with generic models when trained using vast amounts of data and enormous computational resources. But despite many recent triumphs, deep neural networks are difficult to analyze and thus remain mysterious. Most importantly, they lack the robustness, explainability, interpretability, efficiency, and fairness needed for high-stakes decision-making. On the other hand, increasingly realistic model-based approaches—typically derived from first principles and formulated as partial differential equations (PDEs)—are now available for various tasks. One can often calibrate these models—which enable detailed theoretical studies, analysis, and interpretation—with relatively few measurements, thus facilitating their accurate predictions of phenomena. In this talk, I will highlight recent advances and ongoing work to understand and improve deep learning by using techniques from partial differential equations. I will demonstrate how PDE techniques can yield better insight into deep learning algorithms, more robust networks, and more efficient numerical algorithms. I will also expose some of the remaining computational and numerical challenges in this area. — Francesco Tudisco Assistant Professor School of Mathematics GSSI Gran Sasso Science Institute Web: https://ftudisco.gitlab.io <https://ftudisco.gitlab.io> -- You received this message because you are subscribed to the Google Groups "nomads-list" group. To unsubscribe from this group and stop receiving emails from it, send an email to nomads-list+unsubscribe(a)gssi.it. To view this discussion on the web visit https://groups.google.com/a/gssi.it/d/msgid/nomads-list/51fd86c2-9ac2-482f-…. For more options, visit https://groups.google.com/a/gssi.it/d/optout.

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Seminar on 04/06 (Margherita Porcelli)
by Leonardo Robol 04 Jun '21

04 Jun '21

Speaker: Margherita Porcelli Affiliation: Università di Bologna Time: Friday, 04/06/2021, 16:00 Title: Relaxed Interior point methods for low-rank semidefinite programming problems In this talk we will discuss a relaxed variant of interior point methods for semidefinite programming problems (SPDs). We focus on problems in which the primal variable is expected to be low-rank at optimality. Such situations are common in relaxations of combinatorial optimization problems, for example in maximum cut problems as well as in matrix completion problems. We exploit the structure of the sought solution and relax the rigid structure of IPMs for SDP. In anticipation to converging to a low-rank primal solution, a special nearly low-rank form of all primal iterates is imposed. To accommodate such a (restrictive) structure, the first order optimality conditions have to be relaxed and are therefore approximated by solving an auxiliary least-squares problem. The relaxed interior point framework opens numerous possibilities how primal and dual approximated Newton directions can be computed. In particular, it admits the application of both the first- and the second-order methods in this context. In this talk we will focus on second-order approaches and discuss the difficulties arising in the linear algebra phase. A prototype implementation is shown as well as computational results on matrix completion problems. In particular, we will consider mildly-ill conditioned and noisy random problems as well as problems arising in diverse applications as the matrix to be recovered represents city-to- city distances, a grayscale image, game parameters in a basketball tournament. This is joint work with S. Bellavia (Unifi) and J. Gondzio (Univ. Edinburgh) https://www.dm.unipi.it/webnew/it/seminari/relaxed-interior-point-methods-l… Meeting link: https://hausdorff.dm.unipi.it/b/leo-xik-xu4

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Seminar on 14/05 (Alfredo Buttari)
by Leonardo Robol 14 May '21

14 May '21

Speaker: Alfredo Buttari Affiliation: CNRS, IRIT, Toulouse Time: Friday, 14/05/2021, 16:00 Title: Reducing the complexity of linear systems solvers through the block low-rank format Direct linear system solvers are commonly regarded as robust methods for computing the solution of linear systems of equations. Nonetheless, their complexity makes the handling of very large size problems difficult or unfeasible due to excessive execution time or memory consumption. In this talk we discuss the use of low-rank approximation techniques that allow for reducing this complexity at the price of a loss in precision which can be reliably controlled. To take advantage of these low-rank approximations, we have designed a format called block low-rank (BLR) whose objective is to achieve a favorable compromise between complexity and efficiency of operations thanks to its regular structure. We will present the basic BLR format as well as more advanced variants and the associated algorithms; we will analyze their theoretical properties and discuss the issues related to their efficient implementation on parallel computers. We will specifically focus on the use of BLR for the solution of sparse linear systems. The ombination of this format with sparse direct methods, such as the multifrontal one, leads to efficient parallel solvers with scalable complexity. These can either be used as standalone direct solvers or in combination with other techniques such as iterative or multigrid methods. We will present experimental results on real-life problems obtained by integrating the BLR format within the MUMPS parallel sparse direct solver. https://www.dm.unipi.it/webnew/it/seminari/reducing-complexity-linear-syste… Meeting link: https://hausdorff.dm.unipi.it/b/leo-xik-xu4

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Seminar on 07/05 (Stefano Pozza)
by Leonardo Robol 07 May '21

07 May '21

Speaker: Stefano Pozza Affiliation: Charles University, Prague Time: Friday, 07/05/2021, 16:00 Title: The Short-term Rational Lanczos Method and Applications Rational Krylov subspaces have become a reference tool in dimension reduction procedures for several application problems. When data matrices are symmetric, a short-term recurrence can be used to generate an associated orthonormal basis. In the past this procedure was abandoned because it requires twice the number of linear system solves per iteration than with the classical long-term method. We propose an implementation that allows one to obtain key rational subspace matrices without explicitly storing the whole orthonormal basis, with a moderate computational overhead associated with sparse system solves. Several applications are discussed to illustrate the advantages of the proposed procedure. https://www.dm.unipi.it/webnew/it/seminari/short-term-rational-lanczos-meth… Meeting link: https://hausdorff.dm.unipi.it/b/leo-xik-xu4

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Seminar on 23/04 (Philipp Birken)
by Leonardo Robol 23 Apr '21

23 Apr '21

Speaker: Philipp Birken Affiliation: Lund University Time: Friday, 23/04/2021, 16:00 Title: Conservative iterative solvers in computational fluid dynamics The governing equations in computational fluid dynamics such as the Navier-Stokes- or Euler equations are conservation laws. Finite volume methods are designed to respect this and the theorem of Lax-Wendroff underscores the importance of it. It roughly states that for a nonlinear (!) scalar conservation law in 1D , if the numerical method with explicit Euler time integration is consistent and (locally) conservative, then in case of convergence, the numerical method converges to a weak solution. When using implicit time integration, the widespread believe in the community is that conservation is lost. This is however, not necessarily due to the time integration, but due to the use of iterative solvers. We first present a catalogue of iterative solvers that preserve the weaker property of global conservation to identify candidates of solvers that preserve local conservation as used in the Lax-Wendroff theorem. We then proceed to prove an extension of the Lax-Wendroff theorem for the situation that we perform a fixed number of steps of a so called pseudo time iteration per time step. It turns out that in this case, the numerical method converges to a weak solution of the conservation law with a modified propagation speed. This can be exploited to improve performance of the iterative method. https://www.dm.unipi.it/webnew/it/seminari/conservative-iterative-solvers-c… Meeting link: https://hausdorff.dm.unipi.it/b/leo-xik-xu4

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Seminar on 09/04 (Jie Meng)
by Leonardo Robol 09 Apr '21

09 Apr '21

Speaker: Jie Meng Affiliation: Università di Pisa Time: Friday, 09/04/2021, 16:00 Title: Geometric means of quasi-Toeplitz matrices We study means of geometric type of quasi-Toeplitz matrices, that are semi-infinite matrices A = (a_{i,j}) i,j=1,2,... of the form A = T(a) + E, where E represents a compact operator, and T(a) is a semi-infinite Toeplitz matrix associated with the function a, with Fourier series \sum_{l} a_l e^{ilt} , in the sense that (T(a))_{i,j} = a_{j-i}. If a is real valued and essentially bounded, then these matrices represent bounded self-adjoint operators on l^2. We consider the case where a is a continuous function, where quasi-Toeplitz matrices coincide with a classical Toeplitz algebra, and the case where a is in the Wiener algebra, that is, has absolutely convergent Fourier series. We prove that if a_1, ... , a_p are continuous and positive functions, or are in the Wiener algebra with some further conditions, then means of geometric type, such as the ALM, the NBMP and the Karcher mean of quasi-Toeplitz positive definite matrices associated with a_1, ..., a_p , are quasi-Toeplitz matrices associated with the geometric mean (a_1 ... a_p)^{1/p}, which differ only by the compact correction. We show by numerical tests that these operator means can be practically approximated. https://www.dm.unipi.it/webnew/it/seminari/geometric-means-quasi-toeplitz-m… Meeting link: https://hausdorff.dm.unipi.it/b/leo-xik-xu4

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