Related Experiment Video
Updated: Mar 21, 2026
11:00
Experimental Investigation of Secondary Flow Structures Downstream of a Model Type IV Stent Failure in a 180° Curved Artery Test Section
Published on: July 19, 2016
12.0K
A second-order dynamical system for solving inverse quasi-variational inequalities and its application.
Ting Gan1, Vajahat Karim Khan2, Md Kalimuddin Ahmad2
1School of Foreign Languages, Jimei University, Xiamen, China.
Plos One
|March 19, 2026
Summary
This study introduces a dynamical system for solving inverse quasi-variational inequalities (IQVIs). The research confirms the system
Area of Science:
- Numerical analysis
- Optimization theory
- Dynamical systems
Background:
- Inverse quasi-variational inequalities (IQVIs) are crucial in optimization and game theory.
- Solving IQVIs efficiently remains a significant challenge in computational mathematics.
- Dynamical systems offer a novel approach to addressing complex inequality problems.
Purpose of the Study:
- To propose and analyze a second-order dynamical system for solving IQVIs in Hilbert spaces.
- To establish the existence, uniqueness, and stability of solutions for the proposed dynamical system.
- To develop and evaluate a discrete-time algorithm for practical implementation and convergence analysis.
Main Methods:
- Formulation of a second-order dynamical system for IQVIs with strongly monotone and Lipschitz continuous operators.
- Theoretical analysis to prove the existence and uniqueness of strong global solutions.
- Derivation of a discrete-time version leading to a relaxed inertial projection algorithm.
- Lyapunov function-based stability analysis.
- Numerical experiments to validate theoretical findings.
Main Results:
- Existence and uniqueness of strong global solutions for the dynamical system are proven under standard assumptions.
- A discrete-time relaxed inertial projection algorithm is derived, demonstrating linear convergence rates.
- The stability of the dynamical system is rigorously verified using Lyapunov functions.
- Numerical simulations confirm the theoretical predictions and illustrate the system's effectiveness.
Conclusions:
- The proposed second-order dynamical system provides a robust framework for solving IQVIs.
- The derived discrete-time algorithm offers an efficient and convergent method for practical applications.
- The study enhances the understanding of dynamical systems in the context of inequality problems.
Related Concept Videos
01:29Application of Nonlinear Inequalities
290
A nonlinear inequality describes a comparison involving an expression that curves or behaves more complexly than a straight line. These inequalities often appear in forms that include squares, products, or variables in the denominator.To solve such an inequality, one starts by rewriting it so that zero appears on one side. For example, the inequality: can be factored as: This form makes it easier to identify the values that cause the expression to equal zero. In this case, the...
290
01:18Second Order systems II
465
In an underdamped second-order system, where the damping ratio ζ is between 0 and 1, a unit-step input results in a transfer function that, when transformed using the inverse Laplace method, reveals the output response. The output exhibits a damped sinusoidal oscillation, and the difference between the input and output is termed the error signal. This error signal also demonstrates damped oscillatory behavior. Eventually, as the system reaches a steady state, the error diminishes to zero.
465
01:27State Function, Exact and Inexact Differentials
73
A state function is a thermodynamic property that depends solely on the current state of a system, irrespective of its history or how it arrived at that state. These functions are represented by capital letters, such as U, H, and S, which stand for internal energy, enthalpy, and entropy, respectively.For instance, the value of internal energy depends on the system's state variables and remains unaffected by the process path. This means that whether the system underwent a linear process or a...
73
01:22Second Derivatives and Laplace Operator
2.8K
The first order operators using the del operator include the gradient, divergence and curl. Certain combinations of first order operators on a scalar or vector function yield second order expressions. Second-order expressions play a very important role in mathematics and physics. Some second order expressions include the divergence and curl of a gradient function, the divergence and curl of a curl function, and the gradient of a divergence function.
Consider a scalar function. The curl of its...
Consider a scalar function. The curl of its...
2.8K
01:20Introduction to Differential Equations
215
A differential equation is a mathematical expression that establishes a relationship between a function and its derivatives. These equations are fundamental in modeling dynamic systems across various fields of science and engineering. The order of a differential equation is defined by the highest order derivative present in the equation. A first-order differential equation includes only the first derivative, while a second-order differential equation includes up to the second derivative of the...
215
01:20Second Order systems I
712
A servo system exemplifies a second-order system, featuring a proportional controller and load elements that ensure the output position aligns with the input position. The relationship between these components is described by a second-order differential equation. Applying the Laplace transform under zero initial conditions yields the transfer function, showing how inputs are converted to outputs in the system.
By reinterpreting the system, one can derive the closed-loop transfer function, which...
By reinterpreting the system, one can derive the closed-loop transfer function, which...
712