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

Fast Decoupled and DC Powerflow01:24

Fast Decoupled and DC Powerflow

687
The fast decoupled power flow method addresses contingencies in power system operations, such as generator outages or transmission line failures. This method provides quick power flow solutions, essential for real-time system adjustments. Fast decoupled power flow algorithms simplify the Jacobian matrix by neglecting certain elements, leading to two sets of decoupled equations:
687
What is an Electrochemical Gradient?01:26

What is an Electrochemical Gradient?

126.3K
Adenosine triphosphate, or ATP, is considered the primary energy source in cells. However, energy can also be stored in the electrochemical gradient of an ion across the plasma membrane, which is determined by two factors: its chemical and electrical gradients.
The chemical gradient relies on differences in the abundance of a substance on the outside versus the inside of a cell and flows from areas of high to low ion concentration. In contrast, the electrical gradient revolves around an...
126.3K
Gradient and Del Operator01:14

Gradient and Del Operator

4.2K
In mathematics and physics, the gradient and del operator are fundamental concepts used to describe the behavior of functions and fields in space. The gradient is a mathematical operator that gives both the magnitude and direction of the maximum spatial rate of change. Consider a person standing on a mountain. The slope of the mountain at any given point is not defined unless it is quantified in a particular direction. For this reason, a "directional derivative" is defined, which is a vector...
4.2K
Ampere-Maxwell's Law: Problem-Solving01:17

Ampere-Maxwell's Law: Problem-Solving

1.0K
A parallel-plate capacitor with capacitance C, whose plates have area A and separation distance d, is connected to a resistor R and a battery of voltage V. The current starts to flow at t = 0. What is the displacement current between the capacitor plates at time t? From the properties of the capacitor, what is the corresponding real current?
To solve the problem, we can use the equations from the analysis of an RC circuit and Maxwell's version of Ampère's law.
For the first part of the...
1.0K
PD Controller: Design01:26

PD Controller: Design

565
In automotive engineering, car suspension systems often employ Proportional Derivative (PD) controllers to enhance performance. PD controllers are utilized to adjust the damping force in response to road conditions. A controller, acting as an amplifier with a constant gain, demonstrates proportional control, with output directly mirroring input.
Designing a continuous-data controller requires selecting and linking components like adders and integrators, which are fundamental in Proportional,...
565
The Power Flow Problem and Solution01:26

The Power Flow Problem and Solution

767
Power flow problem analysis is fundamental for determining real and reactive power flows in network components, such as transmission lines, transformers, and loads. The power system's single-line diagram provides data on the bus, transmission line, and transformer. Each bus k in the system is characterized by four key variables: voltage magnitude Vk​, phase angle δk​, real power Pk​, and reactive power Qk​. Two of these four variables are inputs, while the power flow program computes...
767

You might also read

Related Articles

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

Sort by
Same author

Fast Reflected Forward-Backward algorithm: achieving fast convergence rates for convex optimization with linear cone constraints.

Journal of scientific computing·2025
Same author

Second Order Splitting Dynamics with Vanishing Damping for Additively Structured Monotone Inclusions.

Journal of dynamics and differential equations·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 journal

A better-than-1.6-approximation for prize-collecting TSP.

Mathematical programming·2026
Same journal

A <math><mrow><mfrac><mn>4</mn> <mn>3</mn></mfrac></mrow></math> -approximation for the maximum leaf spanning arborescence problem in DAGs.

Mathematical programming·2026
Same journal

An FPTAS for Connectivity Interdiction.

Mathematical programming·2026
Same journal

A first order method for linear programming parameterized by circuit imbalance.

Mathematical programming·2026
Same journal

Tight lower bounds for block-structured integer programs.

Mathematical programming·2026
Same journal

Accelerated first-order optimization under nonlinear constraints.

Mathematical programming·2026
See all related articles

Related Experiment Video

Updated: Jan 3, 2026

A Structured Rehabilitation Protocol for Improved Multifunctional Prosthetic Control: A Case Study
06:58

A Structured Rehabilitation Protocol for Improved Multifunctional Prosthetic Control: A Case Study

Published on: November 6, 2015

10.1K

A general double-proximal gradient algorithm for d.c. programming.

Sebastian Banert1, Radu Ioan Boț2

  • 11Department of Mathematics, KTH Royal Institute of Technology, Lindstedtsvägen 25, 100 44 Stockholm, Sweden.

Mathematical Programming
|November 26, 2019
PubMed
Summary
This summary is machine-generated.

This study introduces a new optimization algorithm for difference of convex (d.c.) programs. It uses proximal points for both convex and concave parts, improving upon existing methods and showing cluster points are solutions.

Keywords:
Convergence analysisKurdyka–Łojasiewicz propertyProximal-gradient algorithmToland duald.c. programming

More Related Videos

Dorsal Column Steerability with Dual Parallel Leads using Dedicated Power Sources: A Computational Model
11:19

Dorsal Column Steerability with Dual Parallel Leads using Dedicated Power Sources: A Computational Model

Published on: February 10, 2011

12.2K
Real-Time Proxy-Control of Re-Parameterized Peripheral Signals using a Close-Loop Interface
11:54

Real-Time Proxy-Control of Re-Parameterized Peripheral Signals using a Close-Loop Interface

Published on: May 8, 2021

5.0K

Related Experiment Videos

Last Updated: Jan 3, 2026

A Structured Rehabilitation Protocol for Improved Multifunctional Prosthetic Control: A Case Study
06:58

A Structured Rehabilitation Protocol for Improved Multifunctional Prosthetic Control: A Case Study

Published on: November 6, 2015

10.1K
Dorsal Column Steerability with Dual Parallel Leads using Dedicated Power Sources: A Computational Model
11:19

Dorsal Column Steerability with Dual Parallel Leads using Dedicated Power Sources: A Computational Model

Published on: February 10, 2011

12.2K
Real-Time Proxy-Control of Re-Parameterized Peripheral Signals using a Close-Loop Interface
11:54

Real-Time Proxy-Control of Re-Parameterized Peripheral Signals using a Close-Loop Interface

Published on: May 8, 2021

5.0K

Area of Science:

  • Optimization Theory
  • Applied Mathematics
  • Image Processing

Background:

  • Difference of convex (d.c.) programs are challenging optimization problems.
  • Existing algorithms, like DCA, often rely on subgradient evaluations.
  • Limitations exist in current methods for efficiently handling both convex and concave components.

Purpose of the Study:

  • To propose a novel optimization algorithm for d.c. programs.
  • To enable evaluation of both convex and concave parts using proximal points.
  • To incorporate a smooth part evaluated via its gradient.

Main Methods:

  • Developed a primal-dual splitting-inspired algorithm.
  • Utilizes proximal point evaluations for convex and concave functions.
  • Handles composite concave functions with linear operators separately.

Main Results:

  • Demonstrated that every cluster point of the proposed algorithm is a solution.
  • Established a connection to the Toland dual problem.
  • Proved a descent property for the objective function in a primal-dual formulation.

Conclusions:

  • The new algorithm offers an advancement for optimizing d.c. programs.
  • Convergence is guaranteed under the Kurdyka-Łojasiewicz property.
  • The algorithm shows practical applicability, demonstrated through an image processing model.