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277 discussions

Optimization & Numerical Analysis seminars: Masciotta
by Federico Poloni 29 Feb '16

29 Feb '16

Speaker: Andrea Masciotta Affiliation: Dipartimento di Matematica, Università di Pisa Time: Monday, 7 March 2016, 14:30 Place: Sala Seminari Ovest, Dipartimento di Informatica, Università di Pisa Title: Minimization algorithms for compressive sensing Abstract: Compressive sensing is a new approach to digital signals acquisition and processing. Its main aim is the reconstruction of sparse signals or images (i.e. with few significant coefficients) from what was previously believed to be incomplete information. Compressive sensing has many potential applications, not only limited to the analysis of signals or images. In this talk we will first describe the main theoretical properties of compressive sensing, then three solution algorithms based on \ell_1 minimization will be presented, along with numerical experiments to highlight the main characteristics of these three methods in the framework of compressive sensing. === 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: Miglierina
by Federico Poloni 17 Feb '16

17 Feb '16

Speaker: Enrico Miglierina Affiliation: Università Cattolica del Sacro Cuore, Milano Time: Thursday, 25 February 2016, 15:00 Place: Sala Seminari Est, Dipartimento di Informatica, Università di Pisa Title: Stability by set convergences: from Vector to Set optimization Abstract: (pdf) http://pages.di.unipi.it/fpoloni/files/seminari/Miglierina.pdf The notions of set convergences reveal to be very useful to study stability properties in vector optimization. Indeed, some results that show how the convergence of feasible region implies the convergence of efficient frontiers are known. The oldest ones are based on suitable compactness assumptions that concern the sequence of sets as a whole(see \cite{Attouch-Rihai,Bednarczuk2007,Luc-Lucchetti-Malivert,LoridanMorganRaucci,Penot-Sterna}). Moreover, more recently, some results about convergence of efficient frontiers have been obtained by replacing compactness by convexity (\cite{Lucchetti-Miglierina2004Opt,MM2005}). After a presentation of these results, the last aim of the talk is to extend this class of results to the broader framework of set optimization, that recently received an increasing attention in the literature (\cite{Gutierrez-Miglierina-Molho-Novo}). === Everyone is welcome! -- --federico poloni _______________________________________________ Numpi.di mailing list Numpi.di(a)listgateway.unipi.it http://listgateway.unipi.it/mailman/listinfo/numpi.di

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[Dipartimento.di] Reminder: Optimization & Numerical Analysis seminars: Strabic
by Federico Poloni 18 Dec '15

18 Dec '15

Speaker: Nataša Strabić Affiliation: The University of Manchester Time: Wednesday, December, 9; h. 15:00 Place: Sala Seminari Ovest, Dipartimento di Informatica, Università di Pisa Title: Recent Progress on the Nearest Correlation Matrix Problem Abstract: In a wide range of applications it is required to replace an empirically obtained unit diagonal indefinite symmetric matrix with a valid correlation matrix (unit diagonal positive semidefinite matrix). A popular replacement is the nearest correlation matrix in the Frobenius norm. The first method for computing the nearest correlation matrix with guaranteed convergence was the alternating projections method proposed by Higham in 2002. The rate of convergence of this method is at best linear, and it can require a large number of iterations to converge to within a given tolerance. Although a faster globally convergent Newton algorithm was subsequently developed by Qi and Sun in 2006, the alternating projections method remains very widely used. We show that Anderson acceleration, a technique for accelerating the convergence of fixed-point iterations, can be applied to the alternating projections method and that in practice it brings a significant reduction in both the number of iterations and the computation time. We also show that Anderson acceleration remains effective, and indeed can provide even greater improvements, when it is applied to the variants of the nearest correlation matrix problem in which specified elements are fixed or a lower bound is imposed on the smallest eigenvalue. This is particularly significant for the nearest correlation matrix problem with fixed elements because no Newton method with guaranteed convergence is available for it. Both methods for computing the nearest correlation matrix are based on repeated eigenvalue decompositions and so they can be infeasible in time-critical situations. We have recently proposed an alternative method to restore definiteness to an indefinite matrix called shrinking. The method is based on computing the optimal parameter in a convex linear combination of the indefinite starting matrix and a chosen positive definite target matrix. We show how this problem can be solved by the bisection method and posed as a generalized eigenvalue problem, and we demonstrate how exploiting positive definiteness in these two methods leads to impressive computational savings. The work on these two topics is joint with Nicholas J. Higham, and, for shrinking, with Vedran Šego. === Everyone is welcome! -- --federico poloni Dipartimento di Informatica, Università di Pisa http://www.di.unipi.it/~fpoloni/ tel. +39 050 2213143 ______________________________________________ Dipartimento.di mailing list Dipartimento.di(a)listgateway.unipi.it http://listgateway.unipi.it/mailman/listinfo/dipartimento.di

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[Dipartimento.di] Optimization & Numerical Analysis seminars: Strabic
by Federico Poloni 03 Dec '15

03 Dec '15

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Optimization & Numerical Analysis seminars: Fenu
by Federico Poloni 19 Nov '15

19 Nov '15

Speaker: Caterina Fenu Affiliation: Università di Pisa Time: Thursday, November, 26; 9 am Place: Sala Seminari Ovest, Dipartimento di Informatica, Università di Pisa Title: Fast Computation of Centrality Indices Abstract: One of the main issues in complex networks theory is to find the “most important” nodes. To this aim, one can use matrix functions applied to its adjacency matrix. After an introduction on the use of Gauss-type quadrature rules, we will discuss a new computational method to rank the nodes of both directed and undirected (unweighted) networks according to the values of these functions. The algorithm uses a low-rank approximation of the adjacency matrix, then Gauss quadrature is used to refine the computation. Extended pdf abstract on http://www.di.unipi.it/~fpoloni/files/seminari/Fenu.pdf === 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: Brugiapaglia
by Federico Poloni 23 Oct '15

23 Oct '15

Speaker: Simone Brugiapaglia Affiliation: Politecnico di Milano --- Laboratory for Modeling and Scientific Computing MOX Time: Tuesday, December 15, 11 am Place: Sala Seminari Est, Dipartimento di Informatica, Università di Pisa Title: CORSING: Sparse approximation of PDEs based on Compressed Sensing Abstract: We present a novel method for the numerical approximation of PDEs, motivated by recent developments in sparse representation, and particularly by compressed sensing. We named this approach CORSING (COmpRessed SolvING). Establishing an analogy between the sampling of a signal and the Petrov-Galerkin discretization of a PDE, the CORSING method can recover the best s-term approximation to the solution with respect to N suitable trial functions, with s<<N, by evaluating the bilinear form associated with the PDE against a randomized choice of m<<N test functions. This yields an underdetermined m x N linear system, that is solved by means of sparse optimization techniques. A theoretical analysis of the CORSING procedure is presented, based on the concepts of local a-coherence and restricted inf-sup property, along with numerical experiments that confirm the robustness and reliability of the proposed strategy. === 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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Seminario di Dierk Schleicher
by Dario A. Bini 16 Oct '15

16 Oct '15

Speaker: Dierk Schleicher Title: Newton’s method as an unexpectedly efficient root finder Time: Friday, October 23; 10:00 Place: Aula Magna, Dipartimento di Matematica Abstract: Newton’s method is well known as a root finder locally near the roots. It is often “not recommended” as a global root finder because of its “chaotic” properties. We give a very efficient theoretical upper bound on its speed of convergence: all roots of a degree d polynomial can be found with accuracy eps in O(d^2 log^4 d + d log|\log eps|) Newton iterations in the expected case — very close to the theoretical upper bound of O(d^2) for this method. In practice, all roots of polynomials of degree more than a million are found routinely and in (4log 2) d^2 iterations — in practice, this means less than a day for degree a million on standard laptops. A modified method, for which we do not yet have a complete theory, brings this down to 3 d log^2 d iterations, which in practice for certain polynomials finds all roots of degree a million in a matter of minutes. === Everyone is welcome! Dario A. Bini

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Optimization & Numerical Analysis Seminars: Nesti
by Federico Poloni 14 Sep '15

14 Sep '15

Speaker: Tommaso Nesti (University of Pisa) Title: Numerical methods for computing the steady-state distribution of a G-network. Time: Wednesday, September 23; 16:00 Place: Sala seminari est, informatica Abstract: G-networks are a class of queueing networks introduced by E. Gelembe in 1989, which are characterized by the presence of positive and negative customers. Unlike classical queueing networks, the equations yielding the steady-state distribution of a G-network are nonlinear, resulting in the need of developing efficient numerical methods for their solution. In this talk we present two numerical methods for the computation of the steady-state distribution, namely a fixed point and a Newton-Raphson iteration. Using tools from nonnegative matrix theory, we prove that both methods are locally convergent to the fixed point, with linear and quadratic rate of convergence, respectively. We compare these methods with an existing algorithm, concluding that the Newton-Raphson iteration is a preferable choice for G-networks with a moderate number of queues. We conclude by suggesting a possible application for future research. === 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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Evento AIRO (e conferenza relativa)
by Federico Poloni 31 Aug '15

31 Aug '15

Segnalo anche su questa lista l'evento sociale della conferenza AIRO: http://www.airo.org/conferences/airo2015/e-sport Si tratta di un torneo informale di un videogioco open source che si svolgerà al museo degli strumenti per il calcolo la sera dell'8 settembre. "The competition is open to all the conference participants, the accompanying persons, the organizers, any of their relative, friend and acquaintance (recursively), and whomever can claim any relationship with the conference, however tenuous and imaginative it may be. Fabulous final prices, and gadgets for all participants!" L'evento è collegato alla conferenza dell'AIRO (associazione italiana ricerca operativa) che si svolgerà la prossima settimana al dipartimento di informatica http://www.airo.org/conferences/airo2015/program. Per chi è interessato all'algebra lineare numerica segnalo in particolare il minisimposio "Numerical Methods for Complex Networks", in cui parleranno Francesca Arrigo, Dario Fasino e Caterina Fenu. -federico -- --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: Flores-Bazan and Locatelli
by Federico Poloni 29 Jun '15

29 Jun '15

Two seminars in optimization, one after the other, are taking place next Tuesday. Speaker1: Fabian Flores-Bazan (University of Concepcion) Title1: Strong duality in nonconvex optimization with a single equality and geometric constraints: applications to QP Time1: Tuesday, June 30; 15:00 Place1: Sala seminari est, informatica Speaker2: Marco Locatelli (Università di Parma) Title2: Some results about convex envelopes Time2: Tuesday, June 30; 15:45 Place2: Sala seminari est, informatica Abstract1: The validity of strong duality for a non convex optimization problem under a single equality and geometric constraints is characterized in a topological and geometric manner. In particular, a hidden convexity of the conic hull of joint-range of the pair of functions associated to the original problem, is obtained. Applications to derive KKT conditions without standard constraints qualification are also discussed. Several examples showing our results provide much more information than those appearing elsewhere, are given. Furthermore, first and second order optimality condition, for a non convex quadratic optimization problem under two quadratic equality constraints, are also presented. Finally, the standard quadratic problem involving a non necessarily polyhedral cone is analyzed in detail. The talk is based on joints works with G. Carcamo and F. Opazo. Abstract2: In this talk we discuss convex envelopes for some bivariate functions over general polytopes and for some $n$-dimensional quadratic functions over the unit simplex. We first give two formulations of convex envelope, a primal and a dual one. Next, we discuss how to derive the convex envelope for some bivariate functions over polytopes, provided that some given assumptions are fulfilled. It will turn out that the formula of the convex envelope can be derived through the solution of a parametric convex program or, equivalently, through the solution of the corresponding KKT system. For what concerns the $n$-dimensional quadratic functions over the unit simplex, we will first associate a graph to the quadratic function, and next we will show that the derivation of the convex envelope is related to the identification of the spanning forests over this graph. === 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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