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

Stability of Equilibrium Configuration: Problem Solving01:13

Stability of Equilibrium Configuration: Problem Solving

1.0K
The stability of equilibrium configurations is an important concept in physics, engineering, and other related fields. In simple terms, it refers to the tendency of an object or system to return to its equilibrium position after being disturbed. The stability of an equilibrium configuration can be analyzed by considering the potential energy function of the system and examining its behavior near the equilibrium point.
Problem-solving in the context of the stability of equilibrium configuration...
1.0K
Calculating Equilibrium Concentrations02:05

Calculating Equilibrium Concentrations

53.1K
Being able to calculate equilibrium concentrations is essential to many areas of science and technology—for example, in the formulation and dosing of pharmaceutical products. After a drug is ingested or injected, it is typically involved in several chemical equilibria that affect its ultimate concentration in the body system of interest. Knowledge of the quantitative aspects of these equilibria is required to compute a dosage amount that will solicit the desired therapeutic effect.
A more...
53.1K
Method of Sections: Problem Solving I01:27

Method of Sections: Problem Solving I

1.1K
Consider a symmetrical roof truss structure, composed of vertical, diagonal, and horizontal members. The length of each horizontal member is 4 m. The lengths of the vertical members FB and HD are 4 m, while the length of member GC is 6 m. The loads acting at joints F, G, and H are 2 kN, while those at joints A and E are 1 kN.
1.1K
Method of Joints: Problem Solving I01:30

Method of Joints: Problem Solving I

1.7K
The method of joints is a commonly used technique to analyze the forces in structural trusses. The method is based on the principle of equilibrium, which assumes that the truss members are connected by frictionless pins. The forces at each joint can be determined by considering the equilibrium of the forces acting on that joint. Consider a truss structure with two forces of 20 N and 10 N acting at joints C and D, respectively. The method of joints can be used to determine the forces FCB, FDC,...
1.7K
Method of Joints: Problem Solving II01:30

Method of Joints: Problem Solving II

1.0K
Consider a truss structure with frictionless joints fixed to a wall and roller support. If a force of 150 N is applied to joint A, the forces in each member of the truss can be determined using the method of joints.
1.0K
Method of Sections: Problem Solving II01:30

Method of Sections: Problem Solving II

1.6K
Consider an arbitrary truss structure composed of diagonal, vertical, and horizontal members fixed to the wall. To calculate the force acting on members CB, GB, and GH, method of sections can be used. The loads and lengths of the horizontal and vertical members are known parameters, as shown in the figure.
1.6K

You might also read

Related Articles

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

Sort by
Same author

Strong convergence theorems by hybrid and shrinking projection methods for sums of two monotone operators.

Journal of inequalities and applications·2017
Same journal

The infimum values of two probability functions for the Gamma distribution.

Journal of inequalities and applications·2024
Same journal

The existence of nonnegative solutions for a nonlinear fractional <i>q</i>-differential problem via a different numerical approach.

Journal of inequalities and applications·2021
Same journal

Correction to: On the spectral norms of <i>r</i>-circulant matrices with the bi-periodic Fibonacci and Lucas numbers.

Journal of inequalities and applications·2019
Same journal

Erratum to: General Bahr-Esseen inequalities and their applications.

Journal of inequalities and applications·2019
Same journal

Hermite-Hadamard type inequalities for <i>F</i>-convex function involving fractional integrals.

Journal of inequalities and applications·2019
Same journal

Global maximal inequality to a class of oscillatory integrals.

Journal of inequalities and applications·2019
See all related articles

Related Experiment Video

Updated: Jan 28, 2026

The Innovation Arena: A Method for Comparing Innovative Problem-Solving Across Groups
14:14

The Innovation Arena: A Method for Comparing Innovative Problem-Solving Across Groups

Published on: May 13, 2022

6.4K

Extragradient subgradient methods for solving bilevel equilibrium problems.

Tadchai Yuying1, Bui Van Dinh2, Do Sang Kim3

  • 11Department of Mathematics, Faculty of Science, Naresuan University, Phitsanulok, Thailand.

Journal of Inequalities and Applications
|March 7, 2019
PubMed
Summary
This summary is machine-generated.

This study introduces two novel algorithms for solving bilevel equilibrium problems in Hilbert spaces. Both algorithms demonstrate strong convergence, with the second algorithm achieving this without requiring Lipschitz-type conditions.

Keywords:
Armijo line searchBilevel equilibrium problemsExtragradient Subgradient-Halpern methodsStrong convergence

More Related Videos

Non-equilibrium Microwave Plasma for Efficient High Temperature Chemistry
07:17

Non-equilibrium Microwave Plasma for Efficient High Temperature Chemistry

Published on: August 1, 2017

13.1K
Accurate Determination of the Equilibrium Surface Tension Values with Area Perturbation Tests
07:57

Accurate Determination of the Equilibrium Surface Tension Values with Area Perturbation Tests

Published on: August 30, 2019

7.8K

Related Experiment Videos

Last Updated: Jan 28, 2026

The Innovation Arena: A Method for Comparing Innovative Problem-Solving Across Groups
14:14

The Innovation Arena: A Method for Comparing Innovative Problem-Solving Across Groups

Published on: May 13, 2022

6.4K
Non-equilibrium Microwave Plasma for Efficient High Temperature Chemistry
07:17

Non-equilibrium Microwave Plasma for Efficient High Temperature Chemistry

Published on: August 1, 2017

13.1K
Accurate Determination of the Equilibrium Surface Tension Values with Area Perturbation Tests
07:57

Accurate Determination of the Equilibrium Surface Tension Values with Area Perturbation Tests

Published on: August 30, 2019

7.8K

Area of Science:

  • Optimization
  • Applied Mathematics
  • Functional Analysis

Background:

  • Bilevel equilibrium problems are complex optimization tasks with applications in various fields.
  • Solving these problems efficiently is a significant challenge in mathematical research.
  • Real Hilbert spaces provide a fundamental framework for many mathematical and physical theories.

Purpose of the Study:

  • To propose and analyze novel algorithms for solving bilevel equilibrium problems.
  • To establish conditions for the strong convergence of iterative sequences in these problems.
  • To investigate the impact of specific conditions, like Lipschitz-type, on algorithm performance.

Main Methods:

  • Development of two distinct iterative algorithms.
  • Application of pseudomonotone and Lipschitz-type conditions on bifunctions.
  • Theoretical analysis to prove strong convergence properties.
  • Utilizing concepts from real Hilbert space theory.

Main Results:

  • The first algorithm achieves strong convergence under pseudomonotone and Lipschitz-type conditions.
  • The second algorithm also achieves strong convergence, notably without the need for a Lipschitz-type condition.
  • Both algorithms provide a pathway to finding solutions for bilevel equilibrium problems.

Conclusions:

  • The proposed algorithms offer effective methods for solving bilevel equilibrium problems.
  • The relaxation of the Lipschitz-type condition in the second algorithm broadens its applicability.
  • This research contributes to the advancement of optimization techniques in Hilbert spaces.