- NumPI - Mailing list — Dipartimento di Matematica, UniPI

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

1 0

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

1 0

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

1 0

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

1 0

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

1 0

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

1 0

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

1 0

Fwd: [Dipartimento.di] Avviso Seminario: Leonardo Robol - Seminario di Esperienze di Programmazione
by Federico Poloni 31 Mar '15

31 Mar '15

Inoltro per altri possibili interessati. -------- Forwarded Message -------- Subject: [Dipartimento.di] Avviso Seminario: Leonardo Robol - Seminario di Esperienze di Programmazione Date: Mon, 30 Mar 2015 13:40:22 +0200 From: Gianna M. Del Corso <gianna.delcorso(a)unipi.it> To: dipartimento(a)di.unipi.it Nell'ambito del corso di Esperienze di Programmazione *Mercoledi' 1 Aprile 2015* - ore 11.00 Dip. di Informatica - Aula Seminari EST si terra' il seminario di LEONARDO ROBOL (Scuola Normale Superiore) INTRODUZIONE A JULIA Sarà presentato Julia, un linguaggio per il calcolo scientifico attualmente in fase di sviluppo. Verranno mostrate la sintassi e le principali differenze con i linguaggi attualmente più diffusi, come MATLAB e FORTRAN. Verrà fatta una panoramica delle principale caratteristiche della piattaforma, come i pacchetti aggiuntivi, il notebook IJulia, la gestione dei tipi e il raggiungimento di ottime performance (comparabili a quelle di C e FORTRAN) grazie all'utilizzo di LLVM come backend. Sarà infine presentato qualche esempio per mostrare le potenzialità di Julia per lo sviluppo di codice parallelo. L'interprete è open source e disponibile su http://julialang.org/. ======================== Riferimento: Gianna Del Corso Gianna M. Del Corso, PhD Dipartimento di Informatica, Universita' di Pisa Largo Pontecorvo, 3 56127 Pisa, Italy ph. +39-050-2213118 fax +39-050-2212726 Gianna M. Del Corso, PhD Dipartimento di Informatica, Universita' di Pisa Largo Pontecorvo, 3 56127 Pisa, Italy ph. +39-050-2213118 fax +39-050-2212726

1 0

Optimization & numerical analysis seminars: A. Frangioni
by Federico Poloni 19 Mar '15

19 Mar '15

In the next months we are holding a small cycle of joint seminars between the optimization and numerical analysis groups; their purpose is describing each other's research work, with an eye to possible new common areas of interest. Prof. Frangioni's seminar is the first one of the series. Time: Thursday 2015-Mar-19 (next week), h. 10:00 Place: Sala Seminari Ovest, Dipartimento di Informatica Speaker: Antonio Frangioni, Università di Pisa Title: *Iterative approaches for graph-structured linear systems arising in optimization* Abstract: When applying Interior Point (IP) algorithm to the solution of linear or convex separable optimization problems with strong graph structure, like the Min Cost Flow (MCF) problem, one has to repeatedly solve linear systems with strong graph structure. One of the two possible approach leads to systems with a M-matrix that is basically the weighted Laplacian of the underlying graph, where the weights (but not the graph) change at each iteration of the IP methods and typically become "very imbalanced" at the last ones. For this problem we have used two different techniques: Preconditioned Conjugate Gradient (PCG) methods, based on the idea of extracting a proper triangulated subgraph of the original graph which strictly contains a spanning tree. We have defined a new class of triangulated graphs, called Brother-Connected Trees (BCT), and discuss some fast heuristics for finding BCTs of "large" weight, starting from either the Kruskal algorithm or the Prim one. In addition we have studied multi-iterative techniques where the above PCG approach has been combined with specialized coarser-grid operators which preserve the graph structure of the projected matrix at the inner levels and smoothers, that have been completely characterized. Quite a lot of work still remains to do for understanding which is the best combination of preconditioning and coarsening at different stages of the overarching IP algorithm, implementing these techniques in an efficient solver, and extending them to "truly" interesting graph-structured problems like Multicommodity MCF ones. Everyone is welcome! -- --federico poloni Dipartimento di Informatica, Università di Pisa http://www.di.unipi.it/~fpoloni/ tel:+39-050-2213143

1 1

Seminario del Prof. J. Gondzio 20/3 a Firenze (RETTIFICA AULA)
by margherita porcelli 14 Mar '15

14 Mar '15

Carissimi, vi ricordo il Seminario del Prof. Jacek Gondzio (School of Mathematics, University of Edinburgh) di venerdì prossimo (20/3) a Firenze e, a rettifica di quanto comunicato in precedenza, preciso che il seminario si terrà presso il PLESSO DIDATTICO MORGAGNI (Aula 223). ********************************* Ven 20 Marzo, ore 14:00 Luogo: FIRENZE aula: Aula 223, PLESSO DIDATTICO MORGAGNI Viale Morgagni 40, Università di Firenze TITOLO: "Preconditioners for higher order methods in big data optimization" ABSTRACT: We address efficient preconditioning techniques for the second-order methods applied to solve various sparse approximation problems arising in big data optimization. The preconditioners cleverly exploit special features of such problems and cluster the spectrum of eigenvalues around one. The inexact Newton Conjugate Gradient method excels in these conditions. Numerical results of solving L1-regularization problems of unprecedented sizes will be presented. J. Gondzio joint work K. Fountoulakis ********************************* Cordiali saluti, Margherita Porcelli -- Margherita Porcelli Dipartimento di Matematica Università di Bologna Piazza di Porta S. Donato, 5 40127 - Bologna - Italy phone : +39-051-2094423 home page: http://web.math.unifi.it/users/porcelli ---------------------------------------------------------------- This message was sent using IMP, the Internet Messaging Program.

1 0