News

The following seminar given by our postdoctoral researcher Mehdi Najafi-Kalyani will take place in the Department of Mathematics.

Title: A two-dimensional minimum residual technique for accelerating two-step iterative solvers
Speaker(s): Mehdi Najafi Kalyani, University of Pisa
Date and time: 4 Oct 2024, 11:00 (Europe/Rome)
Lecture series: Seminar on Numerical Analysis
Venue: Dipartimento di Matematica (Aula Seminari).

You can access the full event here: https://events.dm.unipi.it/e/289

Abstract

In this talk, we present a technique to speed up the convergence of a class of two-step iterative methods for solving linear systems of equations. To implement the acceleration technique, the residual norm associated with computed approximations for each sub-iterate is minimized over a certain two-dimensional subspace. Convergence properties of the resulting method will be discussed in detail. It will be further shown that the approach can be developed to solve (regularized) normal equations arising from the discretization of ill-posed problems. Numerical experiments will be disclosed to illustrate the performance of exact and inexact variants of the method for some test problems.

You are very welcome to attend the seminar below

Time: Wednesday 18 September, 15:00
Place: Sala Seminari Ovest, Dipartimento di Informatica

Speaker: Dong Yen Nguyen, University of Hanoi.

Title: “Solving a Class of Nonconvex Quadratic Programs by Inertial DC Algorithms”

Abstract: Two inertial DC algorithms for indefinite quadratic programs under linear constraints (IQPs) are considered in this paper. Using a qualification condition related to the normal cones of unbounded pseudo-faces of the polyhedral convex constraint set, the recession cones of the corresponding faces, and the quadratic form describing the objective function, we prove that the iteration sequences in question are bounded if the given IQP has a finite optimal value. Any cluster point of such a sequence is a KKT point. The convergence of the members of a DCA sequence produced by one of the two inertial algorithms to just one connected component of the KKT point set is also obtained. To do so, we revisit the inertial algorithm for DC programming of de Oliveira and Tcheou [de Oliveira, W., Tcheou, M.P.: An inertial algorithm for DC programming, Set-Valued and Variational Analysis 2019; 27: 895-919] and give a refined version of Theorem 1 from that paper, which can be used for IQPs with unbounded constraint sets. An illustrative example is proposed.

The course “Computational Techniques in Modern Optimization: From Interior Point Methods to Machine Learning and AI” by Prof. Jacek Gondzio from the University of Edinburgh, UK, will be held on 8-11 October 2024 at the university of Trieste, in the context of their PhD programme. A program of the course with timetable is available here.

The organizers invite us to share the announcement: everyone interested is welcome to attend, either in person or online via Microsoft Teams. The link to connect can be obtained by contacting prof. Ángeles Martínez.

The Doctorate School in Computer Science at The University of Pisa is happy to announce the opening of two fully-funded three-years Ph.D. positions (extension to a fourth year if necessary can be considered) on

High-Performance Energy Optimization for Renewable Energy Communities

High-Performance Public Transport Optimization

The positions arise in the context of long-standing research lines. In particular, the first is related with the Italian PNNR “Network 4 Energy Sustainable Transition – NEST”, the PRIN project “Large-scale optimization for sustainable and resilient energy systems”, and the RESILIENT CET Partnership (among others) for the study of optimization of energy systems at all scales, from Renewable Energy Communities to the European level. The second is rather in collaboration with M.A.I.O.R. S.r.L,, an ante-litteram spin-off of the Department of Computer Science of the University of Pisa since over 30 years a leading company in Decision Support Systems for Public Transport companies and regulators, with customers in over 100 cities in Europe, North America, the Middle East, Oceania, South America, and Asia.

Both positions will strive to push the current boundaries of optimization approaches using the innovative C++ software framework SMS++ to develop sophisticated algorithms for large-scale, hard optimization problems. Significant methodological research in fields like decomposition approaches, parallel search, and others (depending on the tastes and inclinations of the students) will have to be conjoined with dedication to significant practical applications and implementation of efficient, well-designed, well-documented, well-tested open-source software.

Details of the call, and about how to apply, can be found at

https://dottorato.unipi.it/index.php/en/application-process-for-the-academic-year-2024-2025/item/874.html

Scroll at the end of the page, click on the “Annexes” link, and search for

INFO05_C INFO06_C

Admission is conditioned on obtaining a Master Degree in any scientific subject by October 31, 2024.

Deadline for the application is August, 22 2024@13:00 (CET).

Potentially interested candidates are very welcome to direct any question to Antonio Frangioni (frangio@di.unipi.it).

A one-day conference about Renewable Energy Communities is organised by the UNESCO Chair (https://unescochair.unipi.it/) on April 22, 2024 at aula A del Polo Congressuale delle Benedettine from 9.30 to 17:00. Participation is free and welcoe.

A call for an RTT (Tenure Track Researcher) position in Numerical Analysis (MAT/08) is open at Department of Computer Science of the University of Pisa.

Deadline for applications: 23 February 2024, 1:00 pm. 

Full regulations and instructions on how to apply are available at https://bandi.unipi.it/public/Bandi/Detail/b34b7404-9d5a-4180-81e2-bd461bfe60a2 .

The procedure is reserved to those who have been employed for at least 36 months on research positions (incl. Phd student positions) at universities and research institutions other than the University of Pisa.

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

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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

https://events.dm.unipi.it/event/225/

On behalf of the organizing committee

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

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ABSTRACT
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.

REGISTRATION AND SUBMISSIONS
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.

PLENARY SPEAKERS
– 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)

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

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

https://events.dm.unipi.it/e/201

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
representation.

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

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