Jove
Visualize
Contact Us
JoVE
x logofacebook logolinkedin logoyoutube logo
ABOUT JoVE
OverviewLeadershipBlogJoVE Help Center
AUTHORS
Publishing ProcessEditorial BoardScope & PoliciesPeer ReviewFAQSubmit
LIBRARIANS
TestimonialsSubscriptionsAccessResourcesLibrary Advisory BoardFAQ
RESEARCH
JoVE JournalMethods CollectionsJoVE Encyclopedia of ExperimentsArchive
EDUCATION
JoVE CoreJoVE BusinessJoVE Science EducationJoVE Lab ManualFaculty Resource CenterFaculty Site
Terms & Conditions of Use
Privacy Policy
Policies

Related Concept Videos

Equilibrium Conditions for a Particle01:23

Equilibrium Conditions for a Particle

When an object is in equilibrium, it is either at rest or moving with a constant velocity. There are two types of equilibrium: static and dynamic. Static equilibrium occurs when an object is at rest, while dynamic equilibrium occurs when an object is moving with a constant velocity. In both cases, there must be a balance of forces acting on the object.
To understand the concept of equilibrium, let us first consider the forces acting on an object. When different forces act on an object, they can...
Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving01:29

Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving

Mechanistic models play a crucial role in algorithms for numerical problem-solving, particularly in nonlinear mixed effects modeling (NMEM). These models aim to minimize specific objective functions by evaluating various parameter estimates, leading to the development of systematic algorithms. In some cases, linearization techniques approximate the model using linear equations.
In individual population analyses, different algorithms are employed, such as Cauchy's method, which uses a...
First Law: Particles in Two-dimensional Equilibrium01:18

First Law: Particles in Two-dimensional Equilibrium

Recall that a particle in equilibrium is one for which the external forces are balanced. Static equilibrium involves objects at rest, and dynamic equilibrium involves objects in motion without acceleration; but it is important to remember that these conditions are relative. For instance, an object may be at rest when viewed from one frame of reference, but that same object would appear to be in motion when viewed by someone moving at a constant velocity.
Newton's first law tells us about the...
Principle of Linear Impulse and Momentum for a Single Particle: Problem Solving01:23

Principle of Linear Impulse and Momentum for a Single Particle: Problem Solving

Consider a wooden box and a cylinder of known masses m1 and m2, respectively, hanging from a ceiling with the help of a massless pulley system.
Lagrange Multipliers: Two Constraints01:28

Lagrange Multipliers: Two Constraints

The method of Lagrange multipliers with two constraints is used to optimize a function subject to two independent constraints. In many applications, the objective function represents a quantity to be maximized or minimized, such as cost, area, distance, or energy. The two constraints represent requirements that the solution must satisfy, such as fixed volume, limited resources, or prescribed dimensions.For a function of three variables, each constraint forms a surface in three-dimensional space.
First Law: Particles in One-dimensional Equilibrium01:10

First Law: Particles in One-dimensional Equilibrium

Newton's first law of motion states that a body at rest remains at rest, or if in motion, remains in motion at constant velocity, unless acted on by a net external force. It also states that there must be a cause for any change in velocity (a change in either magnitude or direction) to occur. This cause is a net external force. For example, consider what happens to an object sliding along a rough horizontal surface. The object quickly grinds to a halt, due to the net force of friction. If we...

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by
Same author

A 3D-1D-0D multiscale model of the neuro-glial-vascular unit for synaptic and vascular dynamics in the dorsal vagal complex.

Journal of mathematical biology·2025
Same author

U-Net-Based Prediction of Cerebrospinal Fluid Distribution and Ventricular Reflux Grading.

NMR in biomedicine·2025
Same author

Directional flow in perivascular networks: mixed finite elements for reduced-dimensional models on graphs.

Journal of mathematical biology·2024
Same author

Calibration of stochastic, agent-based neuron growth models with approximate Bayesian computation.

Journal of mathematical biology·2024
Same author

A comprehensive numerical approach to coil placement in cerebral aneurysms: mathematical modeling and in silico occlusion classification.

Biomechanics and modeling in mechanobiology·2024
Same author

A phase-field model for non-small cell lung cancer under the effects of immunotherapy.

Mathematical biosciences and engineering : MBE·2023

Related Experiment Video

Updated: Jul 10, 2026

Computation of Atmospheric Concentrations of Molecular Clusters from ab initio Thermochemistry
12:11

Computation of Atmospheric Concentrations of Molecular Clusters from ab initio Thermochemistry

Published on: April 8, 2020

Constrained consensus-based optimization and numerical heuristics for the few particle regime.

Jonas Beddrich1, Enis Chenchene2, Massimo Fornasier1,3,4

  • 1Department of Mathematics, Technical University of Munich, Garching by Munich, Germany.

Journal of Global Optimization : an International Journal Dealing with Theoretical and Computational Aspects of Seeking Global Optima and Their Applications in Science, Management and Engineering
|July 9, 2026
PubMed
Summary

Consensus-based optimization (CBO) now solves constrained problems using reflective boundaries, offering global convergence proofs and improved efficiency. This advancement enhances CBO

Keywords:
Consensus-based optimizationConstrained global optimizationHeuristics

More Related Videos

Cryo-EM and Single-Particle Analysis with Scipion
09:06

Cryo-EM and Single-Particle Analysis with Scipion

Published on: May 29, 2021

Related Experiment Videos

Last Updated: Jul 10, 2026

Computation of Atmospheric Concentrations of Molecular Clusters from ab initio Thermochemistry
12:11

Computation of Atmospheric Concentrations of Molecular Clusters from ab initio Thermochemistry

Published on: April 8, 2020

Cryo-EM and Single-Particle Analysis with Scipion
09:06

Cryo-EM and Single-Particle Analysis with Scipion

Published on: May 29, 2021

Area of Science:

  • Numerical analysis
  • Optimization algorithms
  • Computational mathematics

Background:

  • Consensus-based optimization (CBO) is effective for high-dimensional, nonconvex, and nonsmooth unconstrained optimization.
  • Global convergence proofs exist for CBO in unconstrained settings.
  • Adapting CBO for constrained optimization remains a significant challenge.

Purpose of the Study:

  • To extend Consensus-based optimization (CBO) to solve constrained optimization problems.
  • To provide global convergence proofs for CBO in the many-particle regime, including convergence rates.
  • To improve the convergence and computational complexity of CBO, especially in the few-particle regime.

Main Methods:

  • Leveraging reflective boundary conditions for compact and unbounded domains.
  • Developing global convergence proofs for the many-particle regime.
  • Implementing an adaptive region control mechanism.
  • Utilizing geometry-specific random noise, including hierarchical noise structures.
  • Combining with a multigrid finite element method.

Main Results:

  • Global convergence proof for CBO in the many-particle regime with convergence rates.
  • Significant improvements in CBO's convergence and complexity.
  • Successful computation of global minimizers for a challenging constrained p-Allen-Cahn problem with obstacles.
  • Demonstrated effectiveness of reflective boundary conditions and adaptive mechanisms.

Conclusions:

  • The adapted CBO algorithm effectively handles constrained optimization problems.
  • The study provides theoretical guarantees and practical improvements for CBO.
  • The enhanced CBO is capable of solving complex variational problems with obstacles.