• Workshop: Exploiting Algebraic and Geometric Structure in Time-Integration Methods (April 3-5) 1 day ago

    The workshop in the title will take place in the Department of Mathematics next April. We report here the announcement by the organizers.

    Dear colleagues,

    we are happy to announce that the Workshop “Exploiting Algebraic and Geometric Structure in Time-Integration Methods” will be held in Pisa, Italy, on April 03-05, 2024 (the venue will be the Department of Mathematics of the University of Pisa).

    Below, you can find further information about the workshop, alternatively you can visit the web page

    On behalf of the organizing committee

    Michele Benzi
    Nicola Guglielmi
    Santolo Leveque
    Stefano Massei
    Cecilia Pagliantini
    Luca Saluzzi
    Milo Viviani


    The simulation of time-dependent phenomena has become increasingly important in numerous scientific and engineering domains. Efficient and accurate numerical methods are essential for tackling the challenges posed by systems evolving over time. This workshop recognizes the fundamental role played by algebraic and geometric structures in advancing the state-of-the-art in time-integration methods and aims to foster the intellectual exchange and collaboration among the communities of numerical linear algebra, parallel-in-time algorithms, geometric integration, and related disciplines.  
    Over the course of three days, the workshop will feature a series of plenary lectures and talks that delve into the exploitation of hidden or explicit mathematical structures in numerical methods for differential equations. Participants will have the opportunity to share their latest research findings, exchange ideas, and explore interdisciplinary approaches to address the pressing challenges in simulating time-dependent problems.

    The call for registration and submission for contributed talks and posters is now open; the deadline is January 31 2024. Acceptance notification will be sent on February 9 2023.

    Due to logistic constraints, there is a limited number of contributed talks scheduled for the workshop. Submissions will be evaluated by the organizers and, in case, contributed talks might be turned into poster presentations.
    There are no fees for participation, however registration is mandatory.

    – Elena Celledoni (Norwegian University of Science and Technology)
    – Virginie Ehrlacher (Ecole des Ponts ParisTech)
    – Patrick Farrell (University of Oxford)
    – Martin Gander (Université de Genève)
    – Marlis Hochbruck (Karlsruhe Institute of Technology)
    – Christian Lubich (Universität Tübingen)

  • Seminar: On the influence of stochastic rounding bias in implementing gradient descent with applications in low-precision training 5 months ago

    The following seminar will take place at the Department of Mathematics:

    Tuesday 18 July 2023, 14:00. Aula Magna (Dipartimento di Matematica)

    On the influence of stochastic rounding bias in implementing gradient descent with applications in low-precision training

    Lu Xia (Eindhoven University of Technology)

    In the context of low-precision computation for the training of neural networks with the
    gradient descent method (GD), the occurrence of deterministic rounding errors often leads
    to stagnation or adversely affects the convergence of the optimizers. The employ-
    ment of unbiased stochastic rounding (SR) may partially capture gradient updates that
    are lower than the minimum rounding precision, with a certain probability. We
    provide a theoretical elucidation for the stagnation observed in GD when training neural
    networks with low-precision computation. We analyze the impact of floating-point round-
    off errors on the convergence behavior of GD with a particular focus on convex problems.
    Two biased stochastic rounding methods, signed-SR𝜀 and SR𝜀, are proposed, which have
    been demonstrated to eliminate the stagnation of GD and to result in significantly faster
    convergence than SR in low-precision floating-point computation.
    We validate our theoretical analysis by training a binary logistic regression model on
    the Cifar10 database and a 4-layer fully-connected neural network model on the MNIST
    database, utilizing a 16-bit floating-point representation and various rounding techniques.
    The experiments demonstrate that signed-SR𝜀 and SR𝜀 may achieve higher classification
    accuracy than rounding to the nearest (RN) and SR, with the same number of training
    epochs. It is shown that a faster convergence may be obtained by the new rounding
    methods with 16-bit floating-point representation than by RN with 32-bit floating-point

  • Seminar “Submodular maximization of concave utility functions composed with a set-union operator with applications to maximal covering location problems” – canceled 6 months ago

    Unfortunately, due to minor health problems of the speaker, the seminar is canceled. It will hopefully be held at a later date.

  • Seminar: Submodular maximization of concave utility functions composed with a set-union operator with applications to maximal covering location problems 6 months ago

    Relatore: Fabio Furini, Dipartimento di Ingegneria Informatica, Automatica e Gestionale, Università di Roma “La Sapienza”

    Titolo: Submodular maximization of concave utility functions composed with a set-union operator with applications to maximal covering location problems

    Abstract: We study a family of discrete optimization problems asking for the maximization of the expected value of a concave, strictly increasing, and differentiable function composed with a set-union operator. The expected value is computed with respect to a set of coefficients taking values from a discrete set of scenarios. The function models the utility function of the decision maker, while the set-union operator models a covering relationship between two ground sets, a set of items and a set of metaitems. This problem generalizes the problem introduced by Ahmed S, Atamtürk A (Mathematical programming 128(1-2):149–169, 2011), and it can be modeled as a mixed integer nonlinear program involving binary decision variables associated with the items and metaitems. Its goal is to find a subset of metaitems that maximizes the total utility corresponding to the items it covers. It has applications to, among others, maximal covering location, and influence maximization problems. In the paper, we propose a double-hypograph decomposition that allows for projecting out the variables associated with the items by separately exploiting the structural properties of the utility function and of the set-union operator. Thanks to it, the utility function is linearized via an exact outer-approximation technique, whereas the set-union operator is linearized in two ways: either (i) via a reformulation based on submodular cuts, or (ii) via a Benders decomposition. We analyze from a theoretical perspective the strength of the inequalities of the resulting reformulations and embed them into two branch-and-cut algorithms. We also show how to extend our reformulations to the case where the utility function is not necessarily increasing. We then experimentally compare our algorithms inter se, to a standard reformulation based on submodular cuts, to a state-of-the-art global-optimization solver, and to the greedy algorithm for the maximization of a submodular function. The results reveal that, on our testbed, the method based on combining an outer approximation with Benders cuts significantly outperforms the other ones.

    Luogo: Sala Seminari Est, Dipartimento di Informatica, Università di Pisa

    Ora e data: 12:00, Giovedì 15 Giugno 2023

  • Seminar: What do solving train rescheduling problems, designing biomethane production chains, and optimal vehicle fleet acquisition have in common? 7 months ago

    Speaker: Anna Livia Croella

    Date: Monday, May 8 2023, 17:00

    Place: Sala Seminari Ovest

    Abstract/Bio: Anna Livia Croella is a postdoctoral researcher in Operations Research at the University of Pisa, formerly a postdoctoral fellow at La Sapienza University of Rome, where she received her PhD in Operations Research in May 2022 and her B.S. in Management Engineering in October 2017. 

    Her main theoretical interests include Combinatorial Optimization and Mixed Integer Programming. 

    Anna Livia has worked on a diverse portfolio of application issues, covering both industry and society, such as:

    i) train rescheduling problems, she formulated a novel Dynamic Discretization Discovery model with a MaxSAT approach to reschedule train in real-time and outlined an automated procedure to achieve improved system safety in case of a disruption occurrence (a protocol now adopted by a Class I North-American railway);

    ii) location-routing in waste management, she proposed a network design model for a large metropolitan area and a cluster-first location&sizing&route-second approach for designing a biomethane production chain fed by the Organic Fraction of Municipal Solid Waste,
    iii) optimal fleet acquition problem, she formulated a plan for the acquisition of road vehicles by local public transport that, while meeting minimum technical requirements, minimizes the environmental impact of the fleet and its lifespan utility.

  • Date change: MWU 2.0 with approximation guarantee… 8 months ago

    Luca Mencarelli’s seminar is postponed to Monday, May 8.

  • Seminar: MWU 2.0 with approximation guarantee for non-convex (structured) (MI)NLPs 8 months ago

    Luca Mencarelli, a researcher in optimization, has recently joined the department and our laboratory. To welcome him, we have invited him to give a talk on his research. Everyone is welcome to join.

    Date/Time: Wednesday, May 3 Monday, May 8, 2023, 16:00. Date changed!

    Room: Sala Seminari Ovest, Dipartimento di Informatica.

    Title: MWU 2.0 with approximation guarantee for non-convex (structured) (MI)NLPs.

    Speaker: Luca Mencarelli, Department of Computer Science, University of Pisa.

    Abstract: In this talk, we introduce a new approximation guaranteed Multiplicative Weights Updated (MWU) for Mixed Integer Nonlinear Programming (MINLP). We introduce the general MWU framework and we describe its application to two hard global optimization problems, namely the Distance Geometry Problem (DGP) and the (non-convex) Separable Programming (SP). Preliminary yet promising computational results show the potential of the proposed algorithm in terms of efficacy and efficiency for the previous problems.

  • Two seminars at Scuola Normale 10 months ago

    Seminars by two notable researchers in computational mathematics are scheduled for next week in Scuola Normale Superiore:

    Lloyd N. Trefethen, Applications of AAA Rational Approximation
    Tuesday 21/02/2023, 11:00

    Volker Mehrmann, Dirac and Lagrange structures in energy-based mathematical modeling
    Friday 24/02/23, 16:00

    To attend the latter, registration on is required.

  • New results with SMS++ presented 1 year ago

    A presentation at PGMO Days 2022 has showcased the advanced algorithmic capabilities of SMS++ which allowed to exploit HPC architectures to solve huge-scale stochastic programs corresponding to optimal dimensioning of the EU-wide energy system obtaining, in one instance, 600+% improvement in the total (investment + operational) cost.

  • Opening of UNESCO Chair on Energy Communities 1 year ago

    On Wed., October 26@11:00 the opening ceremony of the UNESCO Chair on Energy Communities

    The UNESCO Chair on Sustainable energy communities

    will be held in the Aula Magna of Palazzo della Sapienza. Participation is free for all interested researchers.