A consensus-based model for global optimization and its mean-field limit
From MaRDI portal
Publication:2963631
DOI10.1142/S0218202517400061zbMath1388.90098arXiv1604.05648OpenAlexW2340142742MaRDI QIDQ2963631
Stephan Martin, Oliver Tse, Claudia Totzeck, René Pinnau
Publication date: 15 February 2017
Published in: Mathematical Models and Methods in Applied Sciences (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1604.05648
global optimizationstochastic differential equationsmean-field limitinteracting systemconsensus formation
Nonconvex programming, global optimization (90C26) Asymptotic behavior of solutions to PDEs (35B40) Ordinary differential equations and systems with randomness (34F05)
Related Items
Parameter calibration with stochastic gradient descent for interacting particle systems driven by neural networks ⋮ Constrained Consensus-Based Optimization ⋮ Derivative-Free Bayesian Inversion Using Multiscale Dynamics ⋮ Mean field models for large data-clustering problems ⋮ Efficient derivative-free Bayesian inference for large-scale inverse problems ⋮ Controlled pattern formation of stochastic Cucker-Smale systems with network structures ⋮ Trends in Consensus-Based Optimization ⋮ Binary interaction methods for high dimensional global optimization and machine learning ⋮ Stochastic consensus dynamics for nonconvex optimization on the Stiefel manifold: Mean-field limit and convergence ⋮ Zero-Inertia Limit: From Particle Swarm Optimization to Consensus-Based Optimization ⋮ An analytical framework for consensus-based global optimization method ⋮ Anisotropic Diffusion in Consensus-Based Optimization on the Sphere ⋮ Birth–death dynamics for sampling: global convergence, approximations and their asymptotics ⋮ Neural network approximation: three hidden layers are enough ⋮ Convergence analysis of the discrete consensus-based optimization algorithm with random batch interactions and heterogeneous noises ⋮ Consensus‐based sampling ⋮ On the stochastic robustness of complete clustering predictability for a first‐order consensus model ⋮ On the mean‐field limit for the consensus‐based optimization ⋮ Parameter Calibration with Consensus-Based Optimization for Interaction Dynamics Driven by Neural Networks ⋮ Reproducing kernel Hilbert spaces in the mean field limit ⋮ Consensus-based optimization via jump-diffusion stochastic differential equations ⋮ On the Generalized Langevin Equation for Simulated Annealing ⋮ Kinetic-based optimization enhanced by genetic dynamics ⋮ Swarm-based optimization with random descent ⋮ Collective behaviors of stochastic agent-based models and applications to finance and optimization ⋮ An adaptive consensus based method for multi-objective optimization with uniform Pareto front approximation ⋮ Tikhonov Regularization within Ensemble Kalman Inversion ⋮ On the global convergence of particle swarm optimization methods ⋮ Ensemble-Based Gradient Inference for Particle Methods in Optimization and Sampling ⋮ Modeling behavioral social systems ⋮ Instantaneous control of interacting particle systems in the mean-field limit ⋮ An anisotropic interaction model with collision avoidance ⋮ Challenges in active particles methods: Theory and applications ⋮ Mean Field Limits for Interacting Diffusions with Colored Noise: Phase Transitions and Spectral Numerical Methods ⋮ Unnamed Item ⋮ Convergence and error estimates for time-discrete consensus-based optimization algorithms ⋮ From particle swarm optimization to consensus based optimization: Stochastic modeling and mean-field limit ⋮ A note on the mean-field limit for the particle swarm optimization ⋮ Mean field limits for interacting diffusions in a two-scale potential ⋮ Consensus-based global optimization with personal best ⋮ A multiscale view of nonlinear diffusion in biology: From cells to tissues ⋮ Convergence of a first-order consensus-based global optimization algorithm ⋮ Consensus-based optimization on hypersurfaces: Well-posedness and mean-field limit ⋮ A constrained consensus based optimization algorithm and its application to finance ⋮ One dimensional consensus based algorithm for non-convex optimization ⋮ Constructing Sampling Schemes via Coupling: Markov Semigroups and Optimal Transport ⋮ Emergent behaviors of high-dimensional Kuramoto models on Stiefel manifolds ⋮ Mean-field optimal control for biological pattern formation ⋮ A consensus-based global optimization method for high dimensional machine learning problems ⋮ Propagation of chaos: a review of models, methods and applications. I: Models and methods ⋮ Propagation of chaos: a review of models, methods and applications. II: Applications ⋮ Deep Network With Approximation Error Being Reciprocal of Width to Power of Square Root of Depth ⋮ Mean-Field Optimal Control and Optimality Conditions in the Space of Probability Measures ⋮ Pseudospectral methods and iterative solvers for optimization problems from multiscale particle dynamics ⋮ Convergence analysis of particle swarm optimization in one dimension ⋮ Iterative learning based consensus control for distributed parameter type multi-agent differential inclusion systems with time-delay ⋮ Stochastic gradient descent and fast relaxation to thermodynamic equilibrium: A stochastic control approach ⋮ Mathematical models of self-propelled particles
Uses Software
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Optimization by Simulated Annealing
- A literature survey of benchmark functions for global optimisation problems
- Opinion dynamics and learning in social networks
- Recent approaches to global optimization problems through particle Swarm optimization
- Thermodynamical approach to the travelling salesman problem: An efficient simulation algorithm
- Kinetic description of optimal control problems and applications to opinion consensus
- Modeling opinion dynamics: how the network enhances consensus
- From particle to kinetic and hydrodynamic descriptions of flocking
- Mathematical modeling of collective behavior in socio-economic and life sciences
- On the mathematics of emergence
- Dynamical systems II. Ergodic theory with applications to dynamical systems and statistical mechanics. Transl. from the Russian
- Behavioral crowds: modeling and Monte Carlo simulations toward validation
- An Algorithmic Introduction to Numerical Simulation of Stochastic Differential Equations
- Mathematics, complexity and multiscale features of large systems of self-propelled particles
- Stochastic evolutionary differential games toward a systems theory of behavioral social dynamics
- Opinion Dynamics and the Evolution of Social Power in Influence Networks
- ON A MATHEMATICAL THEORY OF COMPLEX SYSTEMS ON NETWORKS WITH APPLICATION TO OPINION FORMATION
- STOCHASTIC MEAN-FIELD LIMIT: NON-LIPSCHITZ FORCES AND SWARMING
- Heterophilious Dynamics Enhances Consensus
- Asymptotic Flocking Dynamics for the Kinetic Cucker–Smale Model
- On the Modeling of Traffic and Crowds: A Survey of Models, Speculations, and Perspectives
- COOPERATIVE STRATEGIES IN FORMATION OF COMPLEX BACTERIAL PATTERNS
- MODELING CROWD DYNAMICS FROM A COMPLEX SYSTEM VIEWPOINT
- Quantitative Sociodynamics
- A kinetic approach to the study of opinion formation
- Towards consensus: some convergence theorems on repeated averaging
- Mersenne twister
- Discontinuous Galerkin methods
- An analytical framework for consensus-based global optimization method
- Reaching a Consensus
- Emergent Behavior in Flocks
- First‐Order Continuous Models of Opinion Formation
- On the Construction and Comparison of Difference Schemes