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.

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: One Constraint

Lagrange Multipliers: One Constraint

In constrained optimization, the objective is to maximize or minimize a quantity while satisfying a fixed condition. A standard example is a rectangular pen built against a barn wall using 100 meters of fencing. Because the wall provides one side of the enclosure, only the other three sides require fencing. The problem is to find the dimensions that produce the greatest possible area.Let L represent the length parallel to the wall and W the width perpendicular to it. The area of the pen is A =...

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...

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...

Introduction to Nonlinear Inequalities

Introduction to Nonlinear Inequalities

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...

You might also read

Related Articles

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

Sort by

Same author

Reaction of cytochrome bo3 with oxygen: extra redox center(s) are present in the protein.

Biochemistry·1995

Same author

Regulation of striatal cyclic-3',5'-adenosine monophosphate accumulation and GABA release by glutamate metabotropic and dopamine D1 receptors.

The Journal of pharmacology and experimental therapeutics·1995

Same author

Calculation of relative binding free energies and configurational entropies: a structural and thermodynamic analysis of the nature of non-polar binding of thrombin inhibitors based on hirudin55-65.

Journal of molecular biology·1995

Same author

Hydroxylated aromatic inhibitors of HIV-1 integrase.

Journal of medicinal chemistry·1995

Same author

Sevoflurane for outpatient anesthesia: a comparison with propofol.

Anesthesia and analgesia·1995

Same author

Resident bone marrow macrophages produce type 1 interferons that can selectively inhibit interleukin-7-driven growth of B lineage cells.

Immunity·1995

Search research articles

Related Experiment Videos

A recurrent neural network for nonlinear optimization with a continuously differentiable objective function and bound

X B Liang¹, J Wang

¹Department of Electrical and Computer Engineering, University of Delaware, Newark, DE 19716, USA.

IEEE Transactions on Neural Networks

|February 6, 2008

Summary

This summary is machine-generated.

This study introduces a continuous-time recurrent neural network for solving nonlinear optimization problems with bound constraints. The model demonstrates convergence and stability, making it effective for various optimization tasks.

Related Experiment Videos

Area of Science:

Computational Mathematics
Artificial Intelligence
Optimization Theory

Background:

Nonlinear optimization problems with bound constraints are prevalent in various scientific and engineering fields.
Existing methods may face challenges with convergence and stability for complex objective functions.
Recurrent neural networks offer a potential framework for addressing these optimization challenges.

Purpose of the Study:

To propose a novel continuous-time recurrent neural-network model for solving nonlinear optimization problems with bound constraints.
To analyze the theoretical properties of the proposed network, including regularity, completeness, and convergence.
To demonstrate the model's effectiveness through simulations for nonlinear and quadratic optimization tasks.

Main Methods:

Development of a continuous-time recurrent neural network architecture.
Mathematical analysis of network properties: regularity, completeness, primal-dual convergence, and attractivity.
Simulation studies to evaluate performance on nonlinear and strictly convex quadratic optimization problems with bound constraints.

Main Results:

The recurrent neural network model ensures that optima correspond to network equilibria, demonstrating regularity.
For convex objective functions, the network exhibits completeness, with equilibria matching the function's optima.
The network shows primal-dual convergence within the feasible region and attractivity from outside, ensuring stable convergence.
Global exponential stability is proven for minimizing strictly convex quadratic functions under specific network parameters.

Conclusions:

The proposed continuous-time recurrent neural network is a robust tool for nonlinear optimization with bound constraints.
The model's theoretical properties guarantee convergence and stability for a wide range of optimization problems.
Simulation results validate the network's practical performance and potential for real-world applications.