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 …

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 …

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 …

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 …

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 …

Metaheuristic algorithms, widely used for solving complex non-convex and non-
differentiable optimization problems, often lack a solid mathematical foundation. In this …

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 …

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 …

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 …