Giacomo Borghi

Publications

Preprints, published articles, and other scientific work.

Preprints

  1. [1]

    A fast spectral particle method for the Landau equation

    G. Borghi, L. Pareschi

    arXiv preprint, 2026

    arXiv
  2. [2]

    Long-time stability and convergence of particle swarm optimization

    G. Borghi, H. Huang, D. Kim

    arXiv preprint, 2026

    arXiv
  3. [3]

    Two-time-scale learning dynamics: A population view of neural network training

    G. Borghi, H. Im, L. Pareschi

    arXiv preprint, 2026

    arXiv

Journal and conference articles

  1. [4]

    Variational inference via Gaussian interacting particles in the Bures-Wasserstein geometry

    G. Borghi, J. A. Carrillo

    International Conference on Machine Learning, 2026

    OpenReview
  2. [5]

    A particle consensus approach to solving nonconvex-nonconcave min-max problems

    G. Borghi, H. Huang, J. Qiu

    SIAM Journal on Control and Optimization, 64(3), 1573–1601, 2026

    DOI
  3. [6]

    Swarm-based optimization with jumps: A kinetic BGK framework and convergence analysis

    G. Borghi, H. Im, L. Pareschi

    Communications on Pure and Applied Analysis, 31(0), 199–229, 2026

    DOI
  4. [7]

    Chaos propagation in genetic algorithms: An optimal transport approach

    G. Borghi

    Bulletin of the London Mathematical Society, 58(3), e70333, 2026

    DOI
  5. [8]

    Wasserstein convergence rates for stochastic particle approximation of Boltzmann models

    G. Borghi, L. Pareschi

    SIAM Journal on Numerical Analysis, 64(2), 485–509, 2026

    DOI
  6. [9]

    Dynamics of measure-valued agents in the space of probabilities

    G. Borghi, M. Herty, A. Stavitskiy

    SIAM Journal on Mathematical Analysis, 57(5), 5107–5134, 2025

    DOI
  7. [10]

    Kinetic description and convergence analysis of genetic algorithms for global optimization

    G. Borghi, L. Pareschi

    Communications in Mathematical Sciences, 23(3), 641–668, 2025

    Publisher
  8. [11]

    Model predictive control strategies using consensus-based optimization

    G. Borghi, M. Herty

    Mathematical Control and Related Fields, 15(3), 876–894, 2025

    DOI
  9. [12]

    Consensus based optimization with memory effects: Random selection and applications

    G. Borghi, S. Grassi, L. Pareschi

    Chaos, Solitons & Fractals, 174, 113859, 2023

    DOI
  10. [13]

    Repulsion dynamics for uniform Pareto front approximation in multi-objective optimization problems

    G. Borghi

    PAMM, 23(1), e202200285, 2023

    DOI
  11. [14]

    An adaptive consensus based method for multi-objective optimization with uniform Pareto front approximation

    G. Borghi, M. Herty, L. Pareschi

    Applied Mathematics & Optimization, 88(2), 58, 2023

    DOI
  12. [15]

    Constrained consensus-based optimization

    G. Borghi, M. Herty, L. Pareschi

    SIAM Journal on Optimization, 33(1), 211–236, 2023

    DOI
  13. [16]

    A Consensus-Based Algorithm for Multi-Objective Optimization and Its Mean-Field Description

    G. Borghi, M. Herty, L. Pareschi

    2022 IEEE 61st Conference on Decision and Control (CDC), Cancún, Mexico, 4131–4136, 2022

    DOI
  14. [17]

    Binary interaction methods for high dimensional global optimization and machine learning

    A. Benfenati, G. Borghi, L. Pareschi

    Applied Mathematics & Optimization, 86(1), 9, 2022

    DOI

Book chapters and reports

  1. [18]

    Kinetic models for optimization: A unified mathematical framework for metaheuristics

    G. Borghi, M. Herty, L. Pareschi

    EMS Series of Congress Reports, “Modeling, analysis, and control of multi-agent systems across scales”, 2026

    DOI
  2. [19]

    Mini-Workshop: High-Dimensional Control Problems and Mean-Field Equations with Applications in Machine Learning

    G. Borghi, E. Iacomini, M. Oster, C. Segala

    Oberwolfach Reports, 21(4), 3211–3254, 2025

    DOI

Doctoral thesis

  1. [T1]

    Mean-field theory for consensus-based optimization and extensions to constrained and multi-objective problems

    G. Borghi

    Doctoral thesis, RWTH Aachen University, 2024

    Thesis