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

Second Order systems II01:18

Second Order systems II

93
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.
93
Linear Approximation in Time Domain01:21

Linear Approximation in Time Domain

70
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,...
70
Properties of Fourier series II01:21

Properties of Fourier series II

140
Time scaling of signals is a crucial concept in signal processing that affects the Fourier series representation without altering its coefficients. The process modifies the fundamental frequency, thereby changing how the series represents the signal over time. This principle is essential in various applications, including audio and image processing, where signal manipulation is frequent. Understanding function symmetries is fundamental to simplifying the Fourier series.
A function f(t) is...
140
Second Derivatives and Laplace Operator01:22

Second Derivatives and Laplace Operator

1.2K
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...
1.2K
Second Order systems I01:20

Second Order systems I

139
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...
139
Properties of DTFT II01:24

Properties of DTFT II

183
In the study of discrete-time signal processing, understanding the properties of the Discrete-Time Fourier Transform (DTFT) is crucial for analyzing and manipulating signals in the frequency domain. Several properties, including frequency differentiation, convolution, accumulation, and Parseval's relation, offer powerful tools for signal analysis.
The frequency differentiation property is illustrated by considering a DTFT pair and differentiating both sides with respect to ω.
183

You might also read

Related Articles

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

Sort by
Same author

A fast continuous time approach for non-smooth convex optimization using Tikhonov regularization technique.

Computational optimization and applications·2024
Same author

An accelerated minimax algorithm for convex-concave saddle point problems with nonsmooth coupling function.

Computational optimization and applications·2023
Same author

Fast Augmented Lagrangian Method in the convex regime with convergence guarantees for the iterates.

Mathematical programming·2023
Same author

A fast continuous time approach with time scaling for nonsmooth convex optimization.

Advances in continuous and discrete models·2022
Same author

Tikhonov regularization of a second order dynamical system with Hessian driven damping.

Mathematical programming·2021
Same author

Fixing and extending some recent results on the ADMM algorithm.

Numerical algorithms·2021
Same journal

Asymptotic Regularity of a Generalised Stochastic Halpern Scheme.

Journal of optimization theory and applications·2026
Same journal

Optimal Multi-Drug Therapies for Antimicrobial Resistance with Horizontal Transfer.

Journal of optimization theory and applications·2026
Same journal

S-shaped Utility Maximization with VaR Constraint and Partial Information.

Journal of optimization theory and applications·2026
Same journal

A Positive Semidefinite Safe Approximation of Multivariate Distributionally Robust Constraints Determined by Simple Functions.

Journal of optimization theory and applications·2025
Same journal

Generalized Robust Optimization using the Notion of Set-Valued Probability.

Journal of optimization theory and applications·2025
Same journal

ABB Theorems: Results and Limitations in Infinite Dimensions.

Journal of optimization theory and applications·2025
See all related articles

Related Experiment Video

Updated: Jun 13, 2025

Quantifying Cytoskeleton Dynamics Using Differential Dynamic Microscopy
06:37

Quantifying Cytoskeleton Dynamics Using Differential Dynamic Microscopy

Published on: June 15, 2022

3.5K

Second Order Dynamics Featuring Tikhonov Regularization and Time Scaling.

Ernö Robert Csetnek1, Mikhail A Karapetyants1

  • 1Faculty of Mathematics, University of Vienna, Oskar-Morgenstern-Platz 1, 1090 Vienna, Austria.

Journal of Optimization Theory and Applications
|September 9, 2024
PubMed
Summary
This summary is machine-generated.

This study introduces a new second-order differential equation for minimizing nonsmooth convex functions. The novel system enhances convergence rates and proves strong convergence to minimal norm solutions.

Keywords:
Damped inertial dynamicsHessian-driven dampingMoreau envelopeNonsmooth convex optimizationProximal operatorTikhonov regularizationTime scaling

More Related Videos

Control of Cell Adhesion using Hydrogel Patterning Techniques for Applications in Traction Force Microscopy
12:26

Control of Cell Adhesion using Hydrogel Patterning Techniques for Applications in Traction Force Microscopy

Published on: January 29, 2022

5.6K
An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
11:03

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids

Published on: December 4, 2017

8.5K

Related Experiment Videos

Last Updated: Jun 13, 2025

Quantifying Cytoskeleton Dynamics Using Differential Dynamic Microscopy
06:37

Quantifying Cytoskeleton Dynamics Using Differential Dynamic Microscopy

Published on: June 15, 2022

3.5K
Control of Cell Adhesion using Hydrogel Patterning Techniques for Applications in Traction Force Microscopy
12:26

Control of Cell Adhesion using Hydrogel Patterning Techniques for Applications in Traction Force Microscopy

Published on: January 29, 2022

5.6K
An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
11:03

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids

Published on: December 4, 2017

8.5K

Area of Science:

  • Optimization Theory
  • Convex Analysis
  • Differential Equations

Background:

  • Studying dynamical systems for function minimization is crucial in optimization.
  • Second-order differential equations offer advanced convergence properties.
  • Nonsmooth convex optimization presents unique challenges.

Purpose of the Study:

  • To analyze a second-order differential equation with viscous and Hessian-driven damping.
  • To incorporate time scaling and Tikhonov regularization for improved performance.
  • To investigate convergence properties for minimizing nonsmooth convex functions.

Main Methods:

  • Utilizing the Moreau envelope and its gradient properties.
  • Developing a novel second-order differential equation model.
  • Employing analysis within a Hilbert space setting.

Main Results:

  • Demonstrating preservation and improvement of fast convergence rates with time scaling.
  • Proving strong convergence of trajectories to minimal norm solutions.
  • Validating findings through numerical simulations.

Conclusions:

  • The proposed system effectively minimizes nonsmooth convex functions.
  • Time scaling significantly enhances convergence speed.
  • The method converges to the minimum norm solution.