Search research articles

ABOUT JoVE

Overview Leadership Blog JoVE Help Center

AUTHORS

Publishing Process Editorial Board Scope & Policies Peer Review FAQ Submit

LIBRARIANS

Testimonials Subscriptions Access Resources Library Advisory Board FAQ

RESEARCH

JoVE Journal Methods Collections JoVE Encyclopedia of Experiments Archive

EDUCATION

JoVE Core JoVE Business JoVE Science Education JoVE Lab Manual Faculty Resource Center Faculty Site

Terms & Conditions of Use

Related Concept Videos

Application of Nonlinear Inequalities

Application of Nonlinear Inequalities

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...

Optimization Problems

Optimization Problems

Optimization problems often involve identifying maximum or minimum values under specific constraints. A well-known example is determining the longest horizontal pipe that can be moved around a right-angled corner, where a 3-meter-wide hallway meets a 2-meter-wide hallway. This scenario, common in architectural design and industrial transport, can be understood conceptually through geometric and trigonometric reasoning.To visualize the problem, consider the pipe as a straight line that touches...

Implicit Differentiation: Problem Solving

Implicit Differentiation: Problem Solving

Curves defined implicitly, where variables cannot be separated algebraically, require specialized techniques for analysis. The conchoid of Nicomedes exemplifies such a case. Its equation links x and y in a way that prevents isolation of one variable, making implicit differentiation essential to determine the slope and behavior at any point on the curve.The implicit form of the conchoid can be expressed as:To differentiate this equation, y is treated as a function of x, and the chain rule is...

Cartesian Form for Vector Formulation

Cartesian Form for Vector Formulation

The Cartesian form for vector formulation is a process to calculate the moment of force using the position and force vectors. The moment of force is defined as the cross-product of these vectors, making it a vector quantity. The Cartesian form of the position and force vectors involves unit vectors, which can be used to express the cross-product in determinant form.

Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving

Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving

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...

Differential Equations: Problem Solving

Differential Equations: Problem Solving

When analyzing the motion of falling objects, it is essential to consider not only the force of gravity but also the opposing force of air resistance. A practical example involves releasing a heavy test weight during a safety check on a ship. As the weight falls from rest, gravity accelerates it downward while air resistance exerts an upward force that increases with velocity. This dynamic interplay of forces is well described by differential equations, which provide a mathematical framework...

You might also read

Related Articles

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

Sort by

Same author

A multimodal feature disentanglement model for lymphadenopathy diagnosis based on BUS and CDFI ultrasound videos: a retrospective, prospective, multicenter study.

European radiology·2026

Same author

Letter: The Unresolved Issue of NSBB Confounding in Statin Research for Cirrhosis.

Alimentary pharmacology & therapeutics·2026

Same author

Noninvasive blood glucose level estimation using bioimpedance spectroscopy and machine learning: an integrated optimization approach.

Medical engineering & physics·2026

Same author

Nesterov accelerated spectral conjugate gradient algorithm for magnetic resonance imaging with TV regularisation.

Magnetic resonance imaging·2025

Same author

A heart rate variability-driven framework for depression screening leveraging emotion-elicited autonomic divergence.

Journal of physiological anthropology·2025

Same author

Global Trends and Health Inequalities in Acute Hepatitis E Burden: A Joinpoint Regression and Cross-Country Inequality Analysis, 1990-2021.

Journal of viral hepatitis·2025

Search research articles

Related Experiment Video

Updated: Feb 19, 2026

Spatial Multiobjective Optimization of Agricultural Conservation Practices using a SWAT Model and an Evolutionary Algorithm

Spatial Multiobjective Optimization of Agricultural Conservation Practices using a SWAT Model and an Evolutionary Algorithm

Published on: December 9, 2012

A primal-dual algorithm framework for convex saddle-point optimization.

Benxin Zhang¹, Zhibin Zhu²

¹School of Electronic Engineering and Automation, Guangxi Key Laboratory of Automatic Detecting Technology and Instruments, Guilin University of Electronic Technology, Jinji Road, Guilin, China.

Journal of Inequalities and Applications

|November 7, 2017

Summary

This study presents a new primal-dual prediction-correction algorithm framework for convex optimization. The framework unifies existing methods and introduces new ones, proving convergence and analyzing rates.

Keywords:

convex optimization primal-dual method proximal point algorithm variational inequalities

More Related Videos

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

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

Published on: February 10, 2011

A Modeling and Simulation Method for Preliminary Design of an Electro-Variable Displacement Pump

A Modeling and Simulation Method for Preliminary Design of an Electro-Variable Displacement Pump

Published on: June 1, 2022

Related Experiment Videos

Last Updated: Feb 19, 2026

Spatial Multiobjective Optimization of Agricultural Conservation Practices using a SWAT Model and an Evolutionary Algorithm

Spatial Multiobjective Optimization of Agricultural Conservation Practices using a SWAT Model and an Evolutionary Algorithm

Published on: December 9, 2012

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

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

Published on: February 10, 2011

A Modeling and Simulation Method for Preliminary Design of an Electro-Variable Displacement Pump

A Modeling and Simulation Method for Preliminary Design of an Electro-Variable Displacement Pump

Published on: June 1, 2022

Area of Science:

Optimization Theory
Numerical Analysis

Background:

Convex optimization problems with saddle-point structure are common in various scientific fields.
Existing algorithms may lack unified frameworks or specific convergence guarantees.

Purpose of the Study:

Introduce a novel primal-dual prediction-correction algorithm framework.
Unify existing algorithms and generate new primal-dual schemes.
Analyze the convergence properties of the proposed framework.

Main Methods:

Developed a unified primal-dual prediction-correction algorithm framework.
Incorporated proximal terms with positive definite weighting matrices.
Utilized proximal point algorithm-like contraction methods and variational inequalities for convergence analysis.

Main Results:

The proposed framework can derive existing algorithms and create new primal-dual schemes.
Convergence of the framework is proven using two distinct theoretical approaches.
Convergence rates in both ergodic and nonergodic senses were established.

Conclusions:

The introduced primal-dual prediction-correction framework offers a unified approach to convex optimization.
The framework demonstrates theoretical rigor through proven convergence and rate analysis.
This work provides a valuable tool for researchers and practitioners in optimization.