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

Linear time-invariant Systems01:23

Linear time-invariant Systems

A system is linear if it displays the characteristics of homogeneity and additivity, together termed the superposition property. This principle is fundamental in all linear systems. Linear time-invariant (LTI) systems include systems with linear elements and constant parameters.
The input-output behavior of an LTI system can be fully defined by its response to an impulsive excitation at its input. Once this impulse response is known, the system's reaction to any other input can be calculated...
Application of Linearization and Approximation01:29

Application of Linearization and Approximation

A drone flying through complex terrain often relies on more than one sensing method to estimate small changes in altitude. Along with direct measurements, air pressure provides a useful indirect indicator of vertical movement. Atmospheric pressure decreases as altitude increases, and this relationship is commonly described using an exponential model. Although accurate, converting pressure measurements into altitude values requires calculations that are too complex to perform repeatedly during...
Linearization and Approximation01:26

Linearization and Approximation

Linearization is a mathematical technique used to approximate complex, nonlinear functions with simpler linear models in the vicinity of a chosen reference point. The method is based on the idea that, although a function may be difficult to evaluate exactly, its behavior near a specific input value can often be closely approximated by the tangent line at that point. This approach is particularly useful when small deviations from a known value are involved.Consider the square root function, for...
Linear Approximation in Time Domain01:21

Linear Approximation in Time Domain

Nonlinear systems often require sophisticated approaches for accurate modeling and analysis, with state-space representation being particularly effective. This method is especially useful for systems where variables and parameters vary with time or operating conditions, such as in a simple pendulum or a translational mechanical system with nonlinear springs.
For a simple pendulum with a mass evenly distributed along its length and the center of mass located at half the pendulum's length, the...
Linear Approximation in Frequency Domain01:26

Linear Approximation in Frequency Domain

Linear systems are characterized by two main properties: superposition and homogeneity. Superposition allows the response to multiple inputs to be the sum of the responses to each individual input. Homogeneity ensures that scaling an input by a scalar results in the response being scaled by the same scalar.
In contrast, nonlinear systems do not inherently possess these properties. However, for small deviations around an operating point, a nonlinear system can often be approximated as linear.
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...

You might also read

Related Articles

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

Sort by
Same author

Laplacian spectrum constrains collective performance enhancement.

Physical review. E·2026
Same author

Coexistence of many positive invariant sets in several classes of dynamical systems.

Chaos (Woodbury, N.Y.)·2026
Same author

Fuzzy reinforcement learning synchronization of stochastic dynamic networks: An adaptive event-triggered strategy.

Neural networks : the official journal of the International Neural Network Society·2026
Same author

Bipartite Containment of Second-Order Multiagent Systems With Compound Noise Under Fixed or Markovian Switching Signed Topology.

IEEE transactions on cybernetics·2026
Same author

Community structure unveils the path multiplicity in complex networks.

Nature communications·2026
Same author

Symmetry prior based reconstruction of higher-order networks from time-series data.

Chaos (Woodbury, N.Y.)·2026

Related Experiment Videos

A novel recurrent neural network with finite-time convergence for linear programming.

Qingshan Liu1, Jinde Cao, Guanrong Chen

  • 1School of Automation, Southeast University, Nanjing, China. qsliu@seu.edu.cn

Neural Computation
|September 1, 2010
PubMed
Summary

A new recurrent neural network efficiently solves linear programming problems. This gradient-based network guarantees global convergence to exact solutions in finite time, outperforming existing optimization methods.

Related Experiment Videos

Area of Science:

  • Artificial Intelligence
  • Optimization Theory
  • Computational Mathematics

Background:

  • Linear programming (LP) problems are fundamental in optimization.
  • Existing neural network approaches for LP often face challenges with convergence speed and global optimality.
  • There is a need for robust and efficient neural network models for solving LP.

Purpose of the Study:

  • To propose a novel recurrent neural network (RNN) for solving linear programming problems.
  • To establish the finite-time convergence properties of the proposed RNN.
  • To demonstrate the superiority of the new RNN over existing methods.

Main Methods:

  • Development of a recurrent neural network architecture based on the gradient method.
  • Application of Lyapunov stability theory to prove finite-time convergence.
  • Numerical simulations to evaluate performance and compare with existing algorithms.

Main Results:

  • The proposed recurrent neural network demonstrates finite-time convergence.
  • Global convergence to exact optimal solutions is proven.
  • Numerical examples confirm the effectiveness and excellent performance of the new network.

Conclusions:

  • The novel gradient-based recurrent neural network offers a significant advancement in solving linear programming problems.
  • The proven finite-time global convergence is a rare and valuable characteristic for neural network-based optimization.
  • This work provides a powerful new tool for optimization research and applications.