5 papers · 1 filter
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…
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…
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…