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PhD Course: Conic Programming: Theory and applications

Set 232024

Conic Programming: Theory and applications

Prof. Benedetto Manca
Università degli Studi di Cagliari

Abstract

The course covers the theory of conic programming, starting from the simplest case of linear programming and introducing conic quadratic and semi-definite programming. The first part of the course will introduce the theoretical backgrounds needed to define the concept of conic programming. In the second part the case of conic quadratic and semi-definite programming will be addressed together with some applications.

Outline

From Linear to Conic Programming
Conic Quadratic Programming
The quadratic formulation of the Distance Geometry Problem
Semi-definite Programming
The semi-definite relaxation of the Distance Geometry Problem
Diagonally dominant matrices and positive semi-definite matrices
The ellipsoidal separation problem

Schedule

The course consists in 10 hours, two lectures per week. Details will be specified on the occasion of the first lecture, which will be given on October 3, 2024 at 2:30 p.m. in room B of the Department of Mathematics and Computer Science.

Exam

The final exam consists in a presentation on a specific application of conic programming (conic quadratic or semi-definite).

References

Ben-Tal, Aharon, and Arkadi Nemirovski. Lectures on modern convex optimization: analysis, algorithms, and engineering applications. Society for industrial and applied mathematics, 2001.
Liberti, Leo. “Distance geometry and data science.” Top 28.2 (2020): 271-339
Astorino, Annabella, et al. “Ellipsoidal classification via semidefinite programming.” Operations Research Letters 51.2 (2023): 197-203.

PhD Course: Introduction to Kähler Geometry

Set 122024

Introduction to Kähler Geometry

Prof. Roberto Mossa, Prof. Giovanni Placini
Università degli Studi di Cagliari

Abstract

This introductory course covers some of the fundamental concepts of Kähler geometry, with particular attention to almost complex and complex manifolds, the properties of Hermitian metrics, and Kähler metrics. Starting from the basics of differential geometry, we will explore the structure of almost complex and complex manifolds. Subsequently, we will delve into the properties of Hermitian metrics, focusing on the definition and characteristics that define Kähler metrics, which play a key role in integrating the complex structure with the Riemannian one. Through concrete examples and applications, students will gain a deep understanding of these concepts, preparing them for advanced studies in Kähler geometry.

Schedule

January-Febrauary 2025 (TBA)

Exam

The final exam consists in a seminar.

Seminar: Numerical Analysis with Deep Neural Networks

Ago 212024

Numerical Analysis with Deep Neural Networks

Prof. Yuesheng Xu
Old Dominion University and Syracuse University, USA

Abstract

This four-talk lecture sequence aims to introduce numerical analysis with deep neural networks. Traditional function classes used in numerical analysis include polynomials, trigonometric polynomials, splines, finite elements, wavelets, and kernels. Deep neural networks were recently employed in numerical analysis as a class of approximation functions, demonstrating advantages over traditional function classes. These talks will cover the following topics:

Deep neural network representation of a function
Optimization problems that learn a neural network
Adaptive solutions of integral equations with deep neural networks
Adaptive solutions of partial differential equations with deep neural networks.

Schedule

September 12nd, 9.30-11.30 Aula A
September 13nd, 9.30-11.30 Aula A

Seminar: QUBO and Quantum Annealing

Lug 222024

QUBO and Quantum Annealing

Prof. Michele Marchesi
University of Cagliari and NetService spa

Abstract

The seminar, lasting about an hour, presents the problems of unconstrained binary quadratic optimization, where the variables assume binary values (0/1 or -1/1), and the function to be optimized is a quadratic form with real coefficients. It will discuss various real problems that can be represented as QUBO and how to incorporate constraints using penalty coefficients. Exact classical solvers, which can only be used for small problems due to the NP-complete complexity of QUBO problems, and the main heuristic solvers: Tabu Search and Simulated Annealing, will then be presented. Finally, the Quantum Annealing approach for solving this type of problem on specialized quantum computers will be presented.

Schedule

July 25th, 9:30-10:30 (Palazzo delle Scienze, Aula B)

Seminar: Research in Blockchain and Quantum Technologies

Lug 032024

Research in Blockchain and Quantum Technologies

Dr. Ernestas Filatovas
Vilnius University, Lithuania

Abstract

Blockchain and Quantum technologies are among the most groundbreaking advancements, attracting significant attention from industry, government, and academia. This talk highlights the research advances of our “Blockchain and Quantum Technologies Group” in both fields. In the first part of the talk, we introduce Blockchain technology, covering its main concepts such as decentralization, consensus protocols, transaction flow, etc. These key concepts later are summarized within a layered structure. We then present our recent research, including a systematic review and empirical analysis of blockchain simulators, a multi-criteria decision-making (MCDM) framework for selecting consensus protocols, a data-driven classification of consensus protocols using machine learning, and an empirical analysis of wealth decentralization in blockchain networks. This part concludes with an introduction to our novel blockchain-based platform designed to enhance research reproducibility in machine learning. The second part of the talk shifts to Quantum Computing, beginning with an overview of the current state of this technology and its potential applications across various industries. We then highlight our recent achievements, such as the development of more efficient quantum circuits for integer division and the implementation of a quantum blockchain based on hypergraphs. The talk finishes with a presentation of our ongoing research, where we propose an improved quantum annealing method to scale vehicle routing problems.

Schedule

June 20th, 10:00-12:00 (Palazzo delle Scienze, Aula Magna Matematica)

Seminar: From Theory to Practice: Derivative-Free Optimization, Bilevel Problems, and Real-World Applications

Lug 032024

From Theory to Practice: Derivative-Free Optimization, Bilevel Problems, and Real-World Applications

Prof. Remigijus Paulavičius
Vilnius University, Lithuania

Abstract

This talk explores the journey from theory to practice in derivative-free optimization (DFO), primarily focusing on the impact of DIRECT-type algorithms and their application to practical problems. While focusing on this key aspect, the presentation also delves into several other pertinent areas of mathematical optimization, such as bilevel optimization, offering a broader perspective on the field’s advancements and challenges. The presentation begins with an overview of the DIRECT algorithm’s role in DFO, highlighting its strengths and limitations. The subsequent discussion delves into advancements in DIRECT-type algorithms and their integration into software tools, facilitating practical applications. The talk presents a comparative analysis of deterministic and stochastic DFO methods through benchmarking studies, evaluating their performance and suitability for various problem domains. Then, the author showcases his contributions to the bilevel optimization field, where he worked on a general bilevel algorithm and underscored the critical need for such algorithms and software tools in practical applications, including ML. Finally, the talk showcases successful collaborations between academia and industry, highlighting the practical implementation of DFO techniques in real-world scenarios with examples from GlobeTrott Travel and Girteka Logistics, demonstrating the impact of DFO in solving complex optimization problems in business settings.

Schedule

June 19th, 10:00-12:00 (Palazzo delle Scienze, Aula Magna Matematica)

PhD Course: Introduction to scientific Python programming

Giu 172024

Introduction to scientific Python programming

Dr. Tamás László Storcz
University of Pécs, Hungary

Outline

Scientific data and data science, working with Python ecosystem
Data collection, preparation and cleaning
Data visualization
Feature engineering
Creating and validating AI models
Searching model parameters
Practical data management
Examples of application

Schedule

Please register to the course through this form.

June 24th, 15.00-17.00 Aula F
June 25th, 15.00-17.00 Aula F
June 26th, 15.00-17.00 Aula F
June 27th, 9.30-11.30 Aula F
June 28th, 15.00-17.00 Aula F (final test)

Exam

The final exam consists in a test, which will be taken on the last day of the course.

PhD Course: Foundations of Digital Systems and Applications

Giu 172024

Foundations of Digital Systems and Applications

Dr. Zsolt Ercsey
University of Pécs, Hungary

Outline

Introduction to internet technology
Comparison of the business model of mobile operating systems (Android and iOS)
Introduction to a mobile tv recommendation system
Introduction to a sport shooting scheduling system
Solution of a human resource allocation problem

Schedule

Please register to the course through this form.

June 24th, 9.30-11.30 Aula F
June 25th, 9.30-12.30 Aula F
June 26th, 9.30-12.30 Aula F
June 28th, 9.30-11.30 Aula F (final test)

Exam

The final exam consists in a test, which will be taken on the last day of the course.

Seminar: Quantum computing: foundations and state of the art

Mar 072024

Quantum computing: foundations and state of the art

Prof. Michele Marchesi
Dipartimento di Matematica e Informatica
Università degli Studi di Cagliari

Abstract

The seminar is about the current status of Quantum Computing. It will present the math fundamentals of quantum computing, and then will cover Quantum Annealing, which is the current most consolidated application field, featuring working machines with 5000 qbits. The seminar will then cover the current status and possible applications of Quantum Computing, including Shor’s algorithm and the quest for quantum resistant cryptographic algorithms.

Schedule

March, Monday, 11st and Tuesday, 12nd – 17:30-19.00 (Palazzo delle Scienze, Room B)

PhD Course: Isometric Immersions and Harmonic Maps

Feb 172024

Isometric Immersions and Harmonic Maps

Prof. Cezar Oniciuc
Universitatea “Alexandru Ioan Cuza” Iași

Outline

1. Generalities on Riemannian Geometry
2. Isometric immersions (submanifolds) – generalities
3. Special isometric immersions: umbilicals, minimal, CMC
4. Operators on vector bundle
5. Harmonic maps between Riemannian manifolds: first and second variation; fundamental examples

Schedule

May 21st, 16.00-18.00 Aula II
May 22nd, 16.00-18.00 Aula II
May 23rf, 16.00-18.00 Aula II

May 28th, 16.00-18.00 Aula II
May 29th, 16.00-18.00 Aula II
May 30th, 16.00-18.00 Aula II

June 4th, 16.00-18.00 Aula II
June 6th, 16.00-18.00 Aula II

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