On the global convergence of particle swarm optimization methods
In this paper we provide a rigorous convergence analysis for the renowned particle swarm
optimization method by using tools from stochastic calculus and the analysis of partial …
optimization method by using tools from stochastic calculus and the analysis of partial …
Constrained consensus-based optimization
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. A …
constrained nonlinear optimization problems by particle-based gradient-free techniques. A …
Zero-inertia limit: from particle swarm optimization to consensus-based optimization
Recently a continuous description of particle swarm optimization (PSO) based on a system
of stochastic differential equations was proposed by Grassi and Pareschi in [Math. Models …
of stochastic differential equations was proposed by Grassi and Pareschi in [Math. Models …
Mean-field particle swarm optimization
In this chapter we survey some recent results on the global minimization of a non-convex
and possibly non-smooth high dimensional objective function by means of particle-based …
and possibly non-smooth high dimensional objective function by means of particle-based …
Ensemble-based gradient inference for particle methods in optimization and sampling
We propose an approach based on function evaluations and Bayesian inference to extract
higher-order differential information of objective functions from a given ensemble of …
higher-order differential information of objective functions from a given ensemble of …
Kinetic models for optimization: a unified mathematical framework for metaheuristics
Metaheuristic algorithms, widely used for solving complex non-convex and non-
differentiable optimization problems, often lack a solid mathematical foundation. In this …
differentiable optimization problems, often lack a solid mathematical foundation. In this …
Binary interaction methods for high dimensional global optimization and machine learning
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 …
a binary interaction dynamics governed by a Boltzmann type equation. In each interaction …
On the mean field limit of consensus based methods
M Koß, S Weissmann, J Zech - arXiv preprint arXiv:2409.03518, 2024 - arxiv.org
Consensus based optimization (CBO) employs a swarm of particles evolving as a system of
stochastic differential equations (SDEs). Recently, it has been adapted to yield a derivative …
stochastic differential equations (SDEs). Recently, it has been adapted to yield a derivative …
Analysis of a Consensus-based Optimization Method on Hypersurfaces and Applications
P Sünnen - 2023 - mediatum.ub.tum.de
Constrained optimization problems with non-convex cost function are ubiquitous in science
and engineering. One class of methods to solve such optimization problems are so-called …
and engineering. One class of methods to solve such optimization problems are so-called …