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

Lagrange Multipliers: Two Constraints

Lagrange Multipliers: Two Constraints

The method of Lagrange multipliers with two constraints is used to optimize a function subject to two independent constraints. In many applications, the objective function represents a quantity to be maximized or minimized, such as cost, area, distance, or energy. The two constraints represent requirements that the solution must satisfy, such as fixed volume, limited resources, or prescribed dimensions.For a function of three variables, each constraint forms a surface in three-dimensional space.

Gradient Vectors and Their Applications

Gradient Vectors and Their Applications

Every point on a topographical map corresponds to a particular elevation, so the landscape can be modeled as a surface whose height depends on horizontal position. From any given location, a hiker may face infinitely many directions, but only one direction produces the fastest possible increase in elevation. This unique route is called the direction of steepest ascent, and in multivariable calculus, it is represented by the gradient vector of the elevation function.The gradient vector points...

Divergence Theorem in 3D Space

Divergence Theorem in 3D Space

In vector calculus, flux measures the total flow of a vector field through a surface. For a closed surface in three-dimensional space, this means measuring how much of the field passes outward through every point on the boundary. Directly calculating this flux can be difficult when the surface has a complicated or irregular shape. The Divergence Theorem provides a powerful alternative by relating surface flux to behavior inside the enclosed region.The Divergence Theorem states that the outward...

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 key values are 3...

Lagrange Multipliers: Problem Solving

Lagrange Multipliers: Problem Solving

A silo with a cylindrical base, flat bottom, and hemispherical roof is a common design in agricultural and industrial storage due to its structural efficiency and ease of construction. Optimizing its dimensions to maximize storage capacity for a given amount of material—i.e., a fixed surface area—is a classic problem in applied calculus and engineering design. The key parameters are the radius r of the base and the height h of the cylindrical section.The total volume of the silo is obtained by...

Vector Calculus: Problem Solving

Vector Calculus: Problem Solving

Vector calculus provides mathematical tools for analyzing physical fields that vary throughout space. One important application is the study of gravitational interactions between celestial bodies. Consider the Earth positioned at the origin and a satellite located at a point in three-dimensional space. The Earth exerts a gravitational force on the satellite, and this force can be described by components acting along the coordinate directions. Together, these components form a vector field that...

You might also read

Related Articles

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

Sort by

Same author

Multi-Criteria Inverse Robustness in Radiotherapy Planning Using Semidefinite Programming.

ArXiv·2026

Same author

A necessary condition for the guarantee of the superiorization method.

Optimization letters·2025

Same author

GPU-accelerated FREDopt package for simultaneous dose and LET<sub>d</sub> proton radiotherapy plan optimization via superiorization methods.

ArXiv·2025

Same author

General Perturbation Resilient Dynamic String-Averaging for Inconsistent Problems with Superiorization.

Journal of optimization theory and applications·2025

Same author

GPU-accelerated FREDopt package for simultaneous dose and LET<sub>d</sub>proton radiotherapy plan optimization via superiorization methods.

Physics in medicine and biology·2025

Same author

A necessary condition for the guarantee of the superiorization method.

ArXiv·2025

Search research articles

Related Experiment Video

Updated: Jun 15, 2026

Visualization Method for Proprioceptive Drift on a 2D Plane Using Support Vector Machine

Visualization Method for Proprioceptive Drift on a 2D Plane Using Support Vector Machine

Published on: October 27, 2016

On The Behavior of Subgradient Projections Methods for Convex Feasibility Problems in Euclidean Spaces.

Dan Butnariu¹, Yair Censor, Pini Gurfil

¹Department of Mathematics, University of Haifa Mt. Carmel, Haifa 31905, Israel ( dbutnaru@math.haifa.ac.il , yair@math.haifa.ac.il ).

SIAM Journal on Optimization : a Publication of the Society for Industrial and Applied Mathematics

|February 26, 2010

Summary

This study introduces a novel subgradient projection method for convex feasibility problems. The self-adapting strategy ensures algorithmic stability in inconsistent cases, offering computational advantages.

Related Experiment Videos

Last Updated: Jun 15, 2026

Visualization Method for Proprioceptive Drift on a 2D Plane Using Support Vector Machine

Visualization Method for Proprioceptive Drift on a 2D Plane Using Support Vector Machine

Published on: October 27, 2016

Area of Science:

Optimization Theory
Numerical Analysis
Convex Analysis

Background:

Convex feasibility problems (CFPs) are fundamental in optimization.
Existing subgradient projection methods face challenges with general convex sets and inconsistent problems.
Controlling relaxation parameters is crucial for algorithm convergence and stability.

Purpose of the Study:

To develop and analyze subgradient projection methods for CFPs with general convex sets.
To address the challenges posed by inconsistent feasibility problems.
To propose a novel self-adapting strategy for controlling relaxation parameters.

Main Methods:

Investigated subgradient projection algorithms.
Developed a self-adapting strategy for relaxation parameter control.
Analyzed the mathematical behavior of the algorithm in inconsistent cases.
Conducted computational experiments to evaluate performance.

Main Results:

A new subgradient projection strategy with self-adapting relaxation parameters was proposed.
The strategy provides mathematical guarantees for algorithm behavior in inconsistent scenarios.
Numerical results demonstrate significant computational advantages over existing methods.
The method effectively handles general convex sets.

Conclusions:

The proposed self-adapting subgradient projection method offers a robust and efficient solution for convex feasibility problems, particularly in inconsistent cases.
This approach enhances user-flexibility while ensuring algorithmic stability.
The findings suggest practical benefits for various applications requiring feasibility solutions.