17 citations · 32 across the 16 of their papers we have counts for
18 papers
A fast spectral particle method for the Landau equation
Giacomo Borghi, Lorenzo Pareschi
We propose a fast deterministic particle method for the spatially homogeneous Landau equation. The method combines a particle representation of the solution with a Fourier approxim…
Long-time Stability and Convergence of Particle Swarm Optimization
Giacomo Borghi, Hui Huang, Dohyeon Kim
Particle Swarm Optimization (PSO) is a global optimization algorithm defined by an interacting set of particles evolving over the search space. Heuristically motivated, its theoret…
Two-Time-Scale Learning Dynamics: A Population View of Neural Network Training
Giacomo Borghi, Hyesung Im, Lorenzo Pareschi
Population-based learning paradigms, including evolutionary strategies, Population-Based Training (PBT), and recent model-merging methods, combine fast within-model optimisation wi…
Chaos propagation in genetic algorithms: An optimal transport approach
Giacomo Borghi
Genetic algorithms are high-level heuristic optimization methods which enjoy great popularity thanks to their intuitive description, flexibility, and, of course, effectiveness. The…
Variational inference via Gaussian interacting particles in the Bures-Wasserstein geometry
Giacomo Borghi, José A. Carrillo
Motivated by variational inference methods, we propose a zeroth-order algorithm for solving optimization problems in the space of Gaussian probability measures. The algorithm is ba…
Swarm-based optimization with jumps: a kinetic BGK framework and convergence analysis
Giacomo Borghi, Hyesung Im, Lorenzo Pareschi
Metaheuristic algorithms are powerful tools for global optimization, particularly for non-convex and non-differentiable problems where exact methods are often impractical. Particle…
Wasserstein convergence rates for stochastic particle approximation of Boltzmann models
Giacomo Borghi, Lorenzo Pareschi
We establish quantitative convergence rates for stochastic particle approximation based on Nanbu-type Monte Carlo schemes applied to a broad class of collisional kinetic models. Us…
Kinetic models for optimization: a unified mathematical framework for metaheuristics
Giacomo Borghi, Michael Herty, Lorenzo Pareschi
Metaheuristic algorithms, widely used for solving complex non-convex and non-differentiable optimization problems, often lack a solid mathematical foundation. In this review, we ex…
A particle consensus approach to solving nonconvex-nonconcave min-max problems
Giacomo Borghi, Hui Huang, Jinniao Qiu
We propose a zero-order optimization method for sequential min-max problems based on two populations of interacting particles. The systems are coupled so that one population aims t…
Dynamics of measure-valued agents in the space of probabilities
Giacomo Borghi, Michael Herty, Andrey Stavitskiy
Motivated by the development of dynamics in probability spaces, we propose a novel multi-agent dynamic of consensus type where each agent is a probability measure. The agents move…
Model predictive control strategies using consensus-based optimization
Giacomo Borghi, Michael Herty
Model predictive control strategies require to solve in an sequential manner, many, possibly non-convex, optimization problems. In this work, we propose an interacting stochastic a…
Kinetic description and convergence analysis of genetic algorithms for global optimization
Giacomo Borghi, Lorenzo Pareschi
Genetic Algorithms (GA) are a class of metaheuristic global optimization methods inspired by the process of natural selection among individuals in a population. Despite their wides…
Consensus based optimization with memory effects: random selection and applications
Giacomo Borghi, Sara Grassi, Lorenzo Pareschi
In this work we extend the class of Consensus-Based Optimization (CBO) metaheuristic methods by considering memory effects and a random selection strategy. The proposed algorithm i…
Repulsion dynamics for uniform Pareto front approximation in multi-objective optimization problems
Giacomo Borghi
Scalarization allows to solve a multi-objective optimization problem by solving many single-objective sub-problems, uniquely determined by some parameters. In this work, we propose…
An adaptive consensus based method for multi-objective optimization with uniform Pareto front approximation
Giacomo Borghi, Michael Herty, Lorenzo Pareschi
In this work we are interested in stochastic particle methods for multi-objective optimization. The problem is formulated using parametrized, single-objective sub-problems which ar…
A consensus-based algorithm for multi-objective optimization and its mean-field description
Giacomo Borghi, Michael Herty, Lorenzo Pareschi
We present a multi-agent algorithm for multi-objective optimization problems, which extends the class of consensus-based optimization methods and relies on a scalarization strategy…
Constrained consensus-based optimization
Giacomo Borghi, Michael Herty, Lorenzo Pareschi
In this work we are interested in the construction of numerical methods for high dimensional constrained nonlinear optimization problems by particle-based gradient-free techniques.…
Binary interaction methods for high dimensional global optimization and machine learning
Alessandro Benfenati, Giacomo Borghi, Lorenzo Pareschi
In this work we introduce a new class of gradient-free global optimization methods based on a binary interaction dynamics governed by a Boltzmann type equation. In each interaction…