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Fwd: [Dipartimento.di] avviso ciclo di seminari - 8, 10, 11 giugno
by Federico Poloni 04 Jun '15

04 Jun '15

In the framework of the research project "Mathematical models and computational methods for complex networks" by the University of Pisa, Paola Boito (Faculté des Sciences et Techniques Université de Limoges) will give three seminars on "Complex networks, functions of matrices and quadrature rules". The abstract is provided below. The seminars will take place in June at the Department of Computer Science of the University of Pisa: -- June 8th, 15:00-16:00, sala seminari est (room 351); -- June 10th, 10:00-11:00, sala seminari est (room 351); -- June 11th, 15:00-16:00, sala seminari est (room 351). Abstract. One cornerstone of our modern society is the use of different kinds of networks. Our cities are connected by a network of streets and railways, telecommunication networks including their wireless, mobile components, the internet, and the World Wide Web build the most important infrastructure for communication and information worldwide. Designing and managing such networks pose challenging algorithmic and numerical problems. These three talks are concerned with the development, analysis and application of numerical linear algebra tools for the quantitative study of important properties of large-scale complex networks, such as centrality, betweenness and communicability measures. Specifically, we design efficient algorithms for the fast approximation of the entries of matrix functions such as the exponential and the resolvent of adjacency matrices and graph Laplacians, as well as their traces. While these matrices are quite sparse, in the case of complex networks they behave very differently from the matrices associated with regular lattices (grids), such as those arising from discretizations of partial differential equations. Hence, there is a need to develop new methods, both computational and analytical, to deal with these very large-scale problems. Potential applications include the analysis of social networks, the study of biological and neurological networks, applications in physics and operations research, and so forth.

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Optimization & Numerical Analysis Seminar: N. Vannieuwenhoven
by Federico Poloni 03 Jun '15

03 Jun '15

Speaker: Nick Vannieuwenhoven (KU Leuven) Title: Towards a perturbation theory for the tensor rank decomposition Date: Thursday, 4 June 2015. Time: 11:00 Place: Sala Seminari Ovest, dipartimento di informatica Abstract: The tensor rank decomposition is a decomposition of a tensor into a linear combination of rank-1 tensors. One of the key advantages of higher-order tensors is that this decomposition is generally unique, which allows for an interpretation of the individual rank-1 terms. Because of this property, the tensor rank decomposition has found application in several domains. For instance, they can be used as a clustering algorithm in an unsupervised learning setting assuming a certain statistical model wherein each of the rank-1 tensors in the decomposition will correspond with a cluster. In the applications where tensor rank decompositions arise, the tensor is usually known only up to some small perturbation error. This raises the following interesting problem: Suppose that the tensor is perturbed by a small quantity, by how much can the individual rank-1 terms change relative to the magnitude of the perturbation? Can it be unbounded? In this presentation, I will explore the definition of a possible condition number that answers these questions up to first order. == Everyone is welcome! -- --federico poloni Dipartimento di Informatica, Università di Pisa http://www.di.unipi.it/~fpoloni/ tel:+39-050-2213143

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Reminder: Optimization & Numerical Analysis Seminars: F. Romani
by Federico Poloni 13 May '15

13 May '15

Date: Thursday May 14, 2015 Time: 11:00 Place: Sala Seminari Ovest, dipartimento di informatica Speaker: Francesco Romani, dipartimento di informatica, U Pisa. Title: *Krylov subspace methods for the solution of linear systems* Abstract: Krylov subspace methods are iterative methods for the solution of linear systems which operate by multiplying the system matrix (sometimes also its transpose) by a vector. They are recommended when the system matrix is large and sparse or with a strong structure. The most common Krylov subspace methods are presented focusing the attention mainly on the practical and empirical aspects. == The seminar will be in Italian (but with slides in English). Everyone is welcome! -- --federico poloni Dipartimento di Informatica, Università di Pisa http://www.di.unipi.it/~fpoloni/ tel:+39-050-2213143

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Optimization & Numerical Analysis Seminars: F. Romani
by Federico Poloni 07 May '15

07 May '15

Date: Thursday May 14, 2015 Time: 11:00 Place: Sala Seminari Ovest, dipartimento di informatica Speaker: Francesco Romani, dipartimento di informatica, U Pisa. Title: *Krylov subspace methods for the solution of linear systems* Abstract: Krylov subspace methods are iterative methods for the solution of linear systems which operate by multiplying the system matrix (sometimes also its transpose) by a vector. They are recommended when the system matrix is large and sparse or with a strong structure. The most common Krylov subspace methods are presented focusing the attention mainly on the practical and empirical aspects. == The seminar will be in Italian (but with slides in English). Everyone is welcome! -- --federico poloni Dipartimento di Informatica, Università di Pisa http://www.di.unipi.it/~fpoloni/ tel:+39-050-2213143

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Reminder: Optimization & Numerical Analysis Seminar: M.G. Scutellà
by Federico Poloni 29 Apr '15

29 Apr '15

Our next seminar is tomorrow morning. Date: Thursday April 30, 2015 Time: 10:00 Place: Sala Seminari Ovest, dipartimento di informatica Speaker: Maria Grazia Scutellà, dipartimento di informatica, U Pisa. Title: *Optimizing Green Wireless LANs* Abstract: We consider problems arising in the design of Green (or energy-saving) Wireless Local Area Networks (GWLANs). In this context, decisions on powering-on a set of access points, and decisions on the assignment of the user terminals to the opened access points, have to be taken simultaneously. In particular, the level of power assigned to each access point may affect, in a nonlinear way, the capacity of the connections between the access points and the user terminals that are assigned to them. The aim is to minimize the overall power consumption of the access points, which is given by a linear dependency between the power consumed and the total demand assigned to the access points, via assignment costs. In the first part of the talk we present a Mixed Integer formulation with NonLinear constraints (MINLP) and an optimization approach, belonging to the framework of Branch and Benders Cut methods, which is based on the proposed MINLP formulation. In a non-standard fashion, the master problem of the approach includes the variables of the Benders subproblem, but relaxes their integrality. The approach has been tested on a large set of instances, and compared to a more traditional Benders decomposition algorithm on a subset of instances without the assignment costs, where the two approaches can be compared. The main achievements of the computational experimentation are shortly discussed. Then, in the second part of the talk, we address the optimization of GWLANs in a more realistic scenario, which takes into account also some uncertainty factors. Specifically, we present a robust optimization approach that incorporates both link capacity fluctuations and user mobility under Bertsimas and Sim's robust optimization paradigm. Again, preliminary computational results are shortly discussed. === Everyone is welcome! -- --federico poloni Dipartimento di Informatica, Università di Pisa http://www.di.unipi.it/~fpoloni/ tel. +39 050 2213143

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Optimization & Numerical Analysis Seminar: M.G. Scutellà
by Federico Poloni 23 Apr '15

23 Apr '15

Date: Thursday April 30, 2015 Time: 10:00 Place: Sala Seminari Ovest, dipartimento di informatica Speaker: Maria Grazia Scutellà, dipartimento di informatica, U Pisa. Title: *Optimizing Green Wireless LANs* Abstract: We consider problems arising in the design of Green (or energy-saving) Wireless Local Area Networks (GWLANs). In this context, decisions on powering-on a set of access points, and decisions on the assignment of the user terminals to the opened access points, have to be taken simultaneously. In particular, the level of power assigned to each access point may affect, in a nonlinear way, the capacity of the connections between the access points and the user terminals that are assigned to them. The aim is to minimize the overall power consumption of the access points, which is given by a linear dependency between the power consumed and the total demand assigned to the access points, via assignment costs. In the first part of the talk we present a Mixed Integer formulation with NonLinear constraints (MINLP) and an optimization approach, belonging to the framework of Branch and Benders Cut methods, which is based on the proposed MINLP formulation. In a non-standard fashion, the master problem of the approach includes the variables of the Benders subproblem, but relaxes their integrality. The approach has been tested on a large set of instances, and compared to a more traditional Benders decomposition algorithm on a subset of instances without the assignment costs, where the two approaches can be compared. The main achievements of the computational experimentation are shortly discussed. Then, in the second part of the talk, we address the optimization of GWLANs in a more realistic scenario, which takes into account also some uncertainty factors. Specifically, we present a robust optimization approach that incorporates both link capacity fluctuations and user mobility under Bertsimas and Sim's robust optimization paradigm. Again, preliminary computational results are shortly discussed. === Everyone is welcome! -- --federico poloni Dipartimento di Informatica, Università di Pisa http://www.di.unipi.it/~fpoloni/ tel. +39 050 2213143

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Reminder: Optimization & Numerical Analysis Seminar: F. Poloni
by Federico Poloni 16 Apr '15

16 Apr '15

Date: Thursday April 16, 2015 Time: 11:00 Place: Sala Riunioni Est, dipartimento di informatica Speaker: Federico Poloni, dipartimento di informatica, U Pisa. Title: *Methods for accurate invariant subspace computations.* Abstract: We consider two modelling problems, one arising in control theory (linear-quadratic regulator) and one arising in the modelling of queues (or buffers) under a continuous-time Markov model. The solution of both can be reduced to finding the invariant subspace of a suitable structured matrix, or equivalently solving a Riccati-like matrix equation. I will present linear algebra tools that can be used to solve them accurately; in particular: * a QR-like matrix factorization in which a tall skinny n x m matrix is factored as U*R, where R is m x m square invertible and U has a m x m identity submatrix and all its other entries bounded in modulus by 1. This factorization can be formulated as an optimization problem (maximum volume submatrix) or as finding a suitable set of basic variables in a tableau. * (if time allows) a numerical method for the Markov problem based on a technique (GTH method) to solve linear systems with a (possibly ill-conditioned) M-matrix without subtractions, obtaining high accuracy in both large and small entries of the solution. === Everyone is welcome! -- --federico poloni Dipartimento di Informatica, Università di Pisa http://www.di.unipi.it/~fpoloni/ tel. +39 050 2213143

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Optimization & Numerical Analysis Seminar: F. Poloni
by Federico Poloni 10 Apr '15

10 Apr '15

Date: Thursday April 16, 2015 Time: 11:00 Place: Sala Riunioni Est, dipartimento di informatica Speaker: Federico Poloni, dipartimento di informatica, U Pisa. Title: *Methods for accurate invariant subspace computations.* Abstract: We consider two modelling problems, one arising in control theory (linear-quadratic regulator) and one arising in the modelling of queues (or buffers) under a continuous-time Markov model. The solution of both can be reduced to finding the invariant subspace of a suitable structured matrix, or equivalently solving a Riccati-like matrix equation. I will present linear algebra tools that can be used to solve them accurately; in particular: * a QR-like matrix factorization in which a tall skinny n x m matrix is factored as U*R, where R is m x m square invertible and U has a m x m identity submatrix and all its other entries bounded in modulus by 1. This factorization can be formulated as an optimization problem (maximum volume submatrix) or as finding a suitable set of basic variables in a tableau. * (if time allows) a numerical method for the Markov problem based on a technique (GTH method) to solve linear systems with a (possibly ill-conditioned) M-matrix without subtractions, obtaining high accuracy in both large and small entries of the solution. === Everyone is welcome! -- --federico poloni Dipartimento di Informatica, Università di Pisa http://www.di.unipi.it/~fpoloni/ tel. +39 050 2213143

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Reminder: Optimization & Numerical Analysis seminars: R. Vandebril
by Federico Poloni 08 Apr '15

08 Apr '15

Date: Giovedi' 9 Aprile Time: 11:00 Place: Aula Seminari, dipartimento di matematica Speaker: Raf Vandebril, Department of Computer Science, KU Leuven. Title: *The Companion QR* Abstract: In this lecture we will propose a new fast and stable manner of computing roots of polynomials. Roots of polynomials are typically computed by putting the coefficients of the polynomial in the companion matrix and then computing the eigenvalues of this matrix. Exploiting the available low-rank structure leads to an algorithm of quadratic instead of cubic complexity. Several low-cost algorithms have already been proposed. Either they fully exploit the low-rank properties of the involved matrices by representing them for instance via quasiseparable factors, or they write the companion matrix as the sum of a unitary plus low rank matrix and exploit this structure. In this lecture we will use the second manner. However, only a single QR step requires the use of the low rank part. After that we can put the low rank term aside and continue only with the unitary matrix, translating the problem thereby to a unitary eigenvalue problem. Only in the end the low rank matrix is reconstructed to retrieve the eigenvalues. Numerical experiments validate the approach, illustrate its reliability and speed. The algorithm is compared against other available methods and a proof of backward stability is provided. This research is joint work with David S.\ Watkins and Jared L.\ Aurentz from Washington State University, USA and Thomas Mach from the KU Leuven, Belgium. === Everyone is welcome! -- --federico poloni Dipartimento di Informatica, Università di Pisa http://www.di.unipi.it/~fpoloni/ tel:+39-050-2213143

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Optimization & Numerical Analysis seminars: R. Vandebril
by Federico Poloni 01 Apr '15

01 Apr '15

Date: Giovedi' 9 Aprile Time: 11:00 Place: Aula Seminari, dipartimento di matematica Speaker: Raf Vandebril, Department of Computer Science, KU Leuven. Title: *The Companion QR* Abstract: In this lecture we will propose a new fast and stable manner of computing roots of polynomials. Roots of polynomials are typically computed by putting the coefficients of the polynomial in the companion matrix and then computing the eigenvalues of this matrix. Exploiting the available low-rank structure leads to an algorithm of quadratic instead of cubic complexity. Several low-cost algorithms have already been proposed. Either they fully exploit the low-rank properties of the involved matrices by representing them for instance via quasiseparable factors, or they write the companion matrix as the sum of a unitary plus low rank matrix and exploit this structure. In this lecture we will use the second manner. However, only a single QR step requires the use of the low rank part. After that we can put the low rank term aside and continue only with the unitary matrix, translating the problem thereby to a unitary eigenvalue problem. Only in the end the low rank matrix is reconstructed to retrieve the eigenvalues. Numerical experiments validate the approach, illustrate its reliability and speed. The algorithm is compared against other available methods and a proof of backward stability is provided. This research is joint work with David S.\ Watkins and Jared L.\ Aurentz from Washington State University, USA and Thomas Mach from the KU Leuven, Belgium. === Everyone is welcome! -- --federico poloni Dipartimento di Informatica, Università di Pisa http://www.di.unipi.it/~fpoloni/ tel:+39-050-2213143

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