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 Approximation in Time Domain01:21

Linear Approximation in Time Domain

81
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,...
81
Continuous -time Fourier Transform01:11

Continuous -time Fourier Transform

317
The Fourier series is instrumental in representing periodic functions, offering a powerful method to decompose such functions into a sum of sinusoids. This technique, however, necessitates modification when applied to nonperiodic functions. Consider a pulse-train waveform consisting of a series of rectangular pulses. When these pulses have a finite period, they can be accurately represented by a Fourier series. Yet, as the period approaches infinity, resulting in a single, isolated pulse, the...
317
Linear Approximation in Frequency Domain01:26

Linear Approximation in Frequency Domain

91
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....
91
Sampling Continuous Time Signal01:11

Sampling Continuous Time Signal

243
In signal processing, a continuous-time signal can be sampled using an impulse-train sampling technique, followed by the zero-order hold method. Impulse-train sampling involves the use of a periodic impulse train, which consists of a series of delta functions spaced at regular intervals determined by the sampling period. When a continuous-time signal is multiplied by this impulse train, it generates impulses with amplitudes corresponding to the signal's values at the sampling points.
In the...
243
Linear time-invariant Systems01:23

Linear time-invariant Systems

258
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...
258
Basic Continuous Time Signals01:22

Basic Continuous Time Signals

211
Basic continuous-time signals include the unit step function, unit impulse function, and unit ramp function, collectively referred to as singularity functions. Singularity functions are characterized by discontinuities or discontinuous derivatives.
The unit step function, denoted u(t), is zero for negative time values and one for positive time values, exhibiting a discontinuity at t=0. This function often represents abrupt changes, such as the step voltage introduced when turning a car's...
211

You might also read

Related Articles

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

Sort by
Same author

Second Order Dynamics Featuring Tikhonov Regularization and Time Scaling.

Journal of optimization theory and applications·2024
Same author

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

Advances in continuous and discrete models·2022
Same journal

Distributed inexact Newton method with adaptive step sizes.

Computational optimization and applications·2025
Same journal

Off-the-grid regularisation for Poisson inverse problems.

Computational optimization and applications·2025
Same journal

On the SCD semismooth* Newton method for generalized equations with application to a class of static contact problems with Coulomb friction.

Computational optimization and applications·2023
Same journal

On the solution stability of parabolic optimal control problems.

Computational optimization and applications·2023
Same journal

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

Computational optimization and applications·2023
Same journal

Conic formulation of QPCCs applied to truly sparse QPs.

Computational optimization and applications·2023
See all related articles

Related Experiment Video

Updated: Jul 3, 2025

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

5.7K

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

Mikhail A Karapetyants1

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

Computational Optimization and Applications
|February 15, 2024
PubMed
Summary
This summary is machine-generated.

This study introduces a novel optimization method using second-order dynamics and Tikhonov regularization. The approach ensures fast convergence to a minimal norm solution for convex functions.

Keywords:
Damped inertial dynamicsHessian-driven dampingMoreau envelopeNonsmooth convex optimizationProximal operatorStrong convergenceTikhonov regularization

More Related Videos

Deep Neural Networks for Image-Based Dietary Assessment
13:19

Deep Neural Networks for Image-Based Dietary Assessment

Published on: March 13, 2021

9.2K
Design and Application of a Fault Detection Method Based on Adaptive Filters and Rotational Speed Estimation for an Electro-Hydrostatic Actuator
06:45

Design and Application of a Fault Detection Method Based on Adaptive Filters and Rotational Speed Estimation for an Electro-Hydrostatic Actuator

Published on: October 28, 2022

1.6K

Related Experiment Videos

Last Updated: Jul 3, 2025

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

5.7K
Deep Neural Networks for Image-Based Dietary Assessment
13:19

Deep Neural Networks for Image-Based Dietary Assessment

Published on: March 13, 2021

9.2K
Design and Application of a Fault Detection Method Based on Adaptive Filters and Rotational Speed Estimation for an Electro-Hydrostatic Actuator
06:45

Design and Application of a Fault Detection Method Based on Adaptive Filters and Rotational Speed Estimation for an Electro-Hydrostatic Actuator

Published on: October 28, 2022

1.6K

Area of Science:

  • Optimization Theory
  • Convex Analysis
  • Numerical Analysis

Background:

  • Classical optimization problems involve minimizing convex, lower semicontinuous functions.
  • Existing methods may lack guaranteed convergence rates or strong convergence of trajectories.
  • The Moreau envelope and Tikhonov regularization are powerful tools in optimization.

Purpose of the Study:

  • To develop a second-order in time dynamics approach for minimizing convex functions.
  • To combine viscous and Hessian-driven damping with Tikhonov regularization.
  • To achieve fast convergence of function values and strong convergence to a minimal norm solution.

Main Methods:

  • Utilizing the Moreau envelope and its properties for nonsmooth functions.
  • Extending Tikhonov regularization to a nonsmooth setting.
  • Analyzing second-order in time dynamics with combined damping mechanisms.

Main Results:

  • Guaranteed fast convergence of function and Moreau envelope values.
  • Demonstrated strong convergence of system trajectories to a minimal norm solution.
  • Derived precise convergence rates for specific parameter choices.

Conclusions:

  • The proposed dynamical system effectively solves convex optimization problems.
  • The method provides both efficiency (fast convergence) and accuracy (minimal norm solution).
  • Numerical examples validate the theoretical findings and practical applicability.