相关论文: Convergence of Consensus-Based Particle Methods fo…

Bi-level optimization problems, where one wishes to find the global minimizer of an upper-level objective function over the globally optimal solution set of a lower-level objective, arise in a variety of scenarios throughout science and…

This paper presents a particle-based optimization method designed for addressing minimization problems with equality constraints, particularly in cases where the loss function exhibits non-differentiability or non-convexity. The proposed…

We introduce a new stochastic differential model for global optimization of nonconvex functions on compact hypersurfaces. The model is inspired by the stochastic Kuramoto-Vicsek system and belongs to the class of Consensus-Based…

We improve recently introduced consensus-based optimization method, proposed in [R. Pinnau, C. Totzeck, O. Tse and S. Martin, Math. Models Methods Appl. Sci., 27(01):183--204, 2017], which is a gradient-free optimization method for general…

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 to solve the inner maximization problem, while the other aims…

In this paper, we study consensus-based optimization (CBO), which is a multi-agent metaheuristic derivative-free optimization method that can globally minimize nonconvex nonsmooth functions and is amenable to theoretical analysis. Based on…

The recent work arXiv:2407.17373 proposes a derivative-free consensus-based particle method that computes global solutions to nonconvex-nonconcave min-max problems and establishes global exponential convergence in the sense of the…

In this paper, we are interested in finding the global minimizer of a nonsmooth nonconvex unconstrained optimization problem. By combining the discrete consensus-based optimization (CBO) algorithm and the gradient descent method, we develop…

We analyze a zeroth-order particle algorithm for the global optimization of a non-convex function, focusing on a variant of Consensus-Based Optimization (CBO) with small but fixed noise intensity. Unlike most previous studies restricted to…

We investigate the implementation of a new stochastic Kuramoto-Vicsek-type model for global optimization of nonconvex functions on the sphere. This model belongs to the class of Consensus-Based Optimization. In fact, particles move on the…

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 differential equations. Based on a time-continuous formulation…

For algorithms based on interacting particle systems that admit a mean-field description, convergence analysis is often more accessible at the mean-field level. In order to transfer convergence results obtained at the mean-field level to…

In this paper we study convex bi-level optimization problems for which the inner level consists of minimization of the sum of smooth and nonsmooth functions. The outer level aims at minimizing a smooth and strongly convex function over the…

In this paper we are concerned with the global minimization of a possibly non-smooth and non-convex objective function constrained on the unit hypersphere by means of a multi-agent derivative-free method. The proposed algorithm falls into…

Bilevel optimization has been developed for many machine learning tasks with large-scale and high-dimensional data. This paper considers a constrained bilevel optimization problem, where the lower-level optimization problem is convex with…

In this paper, we study a class of bilevel optimization problems, also known as simple bilevel optimization, where we minimize a smooth objective function over the optimal solution set of another convex constrained optimization problem.…

We address an optimization problem where the cost function is the expectation of a random mapping. To tackle the problem two approaches based on the approximation of the objective function by consensus-based particle optimization methods on…

We propose a novel method for sampling and optimization tasks based on a stochastic interacting particle system. We explain how this method can be used for the following two goals: (i) generating approximate samples from a given target…

We analyze the consensus based optimization method proposed by Pinnau et al.(2017) in one dimension. We rigorously provide a quantitative error estimate between the consensus point and global minimizer of a given objective function. Our…

This paper investigates simple bilevel optimization problems where we minimize an upper-level objective over the optimal solution set of a convex lower-level objective. Existing methods for such problems either only guarantee asymptotic…