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

Application of Nonlinear Inequalities01:29

Application of Nonlinear Inequalities

134
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...
134
Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving01:29

Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving

210
Mechanistic models play a crucial role in algorithms for numerical problem-solving, particularly in nonlinear mixed effects modeling (NMEM). These models aim to minimize specific objective functions by evaluating various parameter estimates, leading to the development of systematic algorithms. In some cases, linearization techniques approximate the model using linear equations.
In individual population analyses, different algorithms are employed, such as Cauchy's method, which uses a...
210
Principle of Linear Impulse and Momentum for a Single Particle: Problem Solving01:23

Principle of Linear Impulse and Momentum for a Single Particle: Problem Solving

874
Consider a wooden box and a cylinder of known masses m1 and m2, respectively,  hanging from a ceiling with the help of a massless pulley system.
874
Introduction to Nonlinear Inequalities01:25

Introduction to Nonlinear Inequalities

102
Linear and nonlinear inequalities are fundamental for analyzing variable relationships and identifying ranges satisfying specific conditions. A linear inequality involves variables raised only to the first power, resulting in a straight-line graph. This line partitions the coordinate plane into two distinct regions: one that satisfies the inequality and one that does not. Each region represents a set of solutions where the linear relationship holds true under the specified constraint.Nonlinear...
102
Kinematic Equations: Problem Solving01:15

Kinematic Equations: Problem Solving

27.0K
When analyzing one-dimensional motion with constant acceleration, the problem-solving strategy involves identifying the known quantities and choosing the appropriate kinematic equations to solve for the unknowns. Either one or two kinematic equations are needed to solve for the unknowns, depending on the known and unknown quantities. Generally, the number of equations required is the same as the number of unknown quantities in the given example. Two-body pursuit problems always require two...
27.0K
Constraints and Statical Determinacy01:26

Constraints and Statical Determinacy

883
In structural engineering, the equilibrium of a system is not only determined by its equations of equilibrium but also with the help of constraints. Constraints refer to restrictions on the motion of a system. The proper combinations of constraints can minimize the total number of constraints needed to maintain a system in mechanical equilibrium. When this happens, the system is said to be statically determinate. For such systems, the unknown reaction supports can be estimated using equilibrium...
883

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 Dynamics Featuring Tikhonov Regularization and Time Scaling.

Journal of optimization theory and applications·2024
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 journal

Quartic Regularity.

Vietnam journal of mathematics·2025
Same journal

Strongly Base-Two Groups.

Vietnam journal of mathematics·2023
Same journal

Bounds for the Diameters of Orbital Graphs of Affine Groups.

Vietnam journal of mathematics·2023
Same journal

A Computational Study of Blood Flow Dynamics in the Pulmonary Arteries.

Vietnam journal of mathematics·2022
Same journal

Conservation of Forces and Total Work at the Interface Using the Internodes Method.

Vietnam journal of mathematics·2022
Same journal

How to Best Choose the Outer Coarse Mesh in the Domain Decomposition Method of Bank and Jimack.

Vietnam journal of mathematics·2022
See all related articles

Related Experiment Video

Updated: Dec 13, 2025

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

2.0K

An Inertial Proximal-Gradient Penalization Scheme for Constrained Convex Optimization Problems.

Radu Ioan Boţ1, Ernö Robert Csetnek1, Nimit Nimana2

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

Vietnam Journal of Mathematics
|July 28, 2020
PubMed
Summary
This summary is machine-generated.

We introduce a new algorithm for solving complex bilevel optimization problems. This method uses penalization and memory effects to ensure convergence to the best possible solution.

Keywords:
Fenchel conjugateInertial algorithmPenalizationProximal-gradient algorithm

More Related Videos

Gain-compensation Methodology for a Sinusoidal Scan of a Galvanometer Mirror in Proportional-Integral-Differential Control Using Pre-emphasis Techniques
09:01

Gain-compensation Methodology for a Sinusoidal Scan of a Galvanometer Mirror in Proportional-Integral-Differential Control Using Pre-emphasis Techniques

Published on: April 4, 2017

9.0K
Deep Neural Networks for Image-Based Dietary Assessment
13:19

Deep Neural Networks for Image-Based Dietary Assessment

Published on: March 13, 2021

9.8K

Related Experiment Videos

Last Updated: Dec 13, 2025

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

2.0K
Gain-compensation Methodology for a Sinusoidal Scan of a Galvanometer Mirror in Proportional-Integral-Differential Control Using Pre-emphasis Techniques
09:01

Gain-compensation Methodology for a Sinusoidal Scan of a Galvanometer Mirror in Proportional-Integral-Differential Control Using Pre-emphasis Techniques

Published on: April 4, 2017

9.0K
Deep Neural Networks for Image-Based Dietary Assessment
13:19

Deep Neural Networks for Image-Based Dietary Assessment

Published on: March 13, 2021

9.8K

Area of Science:

  • Optimization Theory
  • Convex Analysis
  • Numerical Analysis

Background:

  • Bilevel optimization problems involve nested objective functions, making them challenging to solve.
  • Existing methods often struggle with convergence guarantees for complex objective functions.

Purpose of the Study:

  • To develop a novel proximal-gradient algorithm for a specific class of bilevel optimization problems.
  • To analyze the convergence properties of the proposed algorithm.

Main Methods:

  • A proximal-gradient algorithm incorporating penalization terms.
  • Inertial and memory effects are included to enhance convergence.
  • Analysis of weak convergence for iterates and objective function values.

Main Results:

  • The proposed algorithm is designed for minimizing the sum of a proper, convex, lower semicontinuous function and a convex differentiable function.
  • Convergence is demonstrated under suitable choices of step sizes and penalization parameters.
  • Weak convergence of iterates to an optimal solution and convergence of objective function values to the optimal value are proven.

Conclusions:

  • The developed algorithm provides a robust method for addressing challenging bilevel optimization problems.
  • The theoretical analysis confirms the algorithm's effectiveness in finding optimal solutions.