Lagrange multipliers

E156182

constrained optimization method mathematical technique optimization method

Lagrange multipliers are a mathematical optimization technique used to find the extrema of functions subject to equality constraints.

Try in SPARQL Jump to: Surface forms Disambiguation Statements Elicitation Referenced by

All labels observed (3)

Label	Occurrences
Lagrange multipliers canonical	5
Lagrange duality	1
Lagrange multiplier rule	1

How this entity was disambiguated

This entity first appeared as the object of triple T1358583 — resolving that mention is where its identity was fixed. The disambiguator weighed these candidate entities and picked the highlighted one (or “None”, minting a new entity). This is how homonymy is resolved: the same surface form can point to different entities.

NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07

Target entity: Lagrange multipliers
Context triple: [Joseph-Louis Lagrange, knownFor, Lagrange multipliers]

A. Karush–Kuhn–Tucker conditions
The Karush–Kuhn–Tucker conditions are fundamental optimality criteria in nonlinear programming that generalize Lagrange multipliers to handle inequality constraints.
B. Euler–Lagrange equation
The Euler–Lagrange equation is a fundamental differential equation in the calculus of variations that provides the condition for a function to make a functional stationary, forming the basis of Lagrangian mechanics and many physical theories.
C. Laplace operator
The Laplace operator is a second-order differential operator widely used in mathematics and physics to describe phenomena such as diffusion, heat flow, and wave propagation.
D. Laplace equation
The Laplace equation is a fundamental second-order partial differential equation widely used in physics and engineering to describe steady-state phenomena such as electrostatics, gravitation, and heat conduction.
E. Hessian forces
Hessian forces were German auxiliary troops hired by the British Crown during the American Revolutionary War, known for their disciplined fighting and prominent role in key battles such as Trenton.
F. None of above. chosen
G. Unsure - the case is ambiguous/there is not enough information to decide.

NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07

Target entity: Lagrange multipliers
Target entity description: Lagrange multipliers are a mathematical optimization technique used to find the extrema of functions subject to equality constraints.

A. Karush–Kuhn–Tucker conditions
The Karush–Kuhn–Tucker conditions are fundamental optimality criteria in nonlinear programming that generalize Lagrange multipliers to handle inequality constraints.
B. Euler–Lagrange equation
The Euler–Lagrange equation is a fundamental differential equation in the calculus of variations that provides the condition for a function to make a functional stationary, forming the basis of Lagrangian mechanics and many physical theories.
C. Laplace operator
The Laplace operator is a second-order differential operator widely used in mathematics and physics to describe phenomena such as diffusion, heat flow, and wave propagation.
D. Laplace equation
The Laplace equation is a fundamental second-order partial differential equation widely used in physics and engineering to describe steady-state phenomena such as electrostatics, gravitation, and heat conduction.
E. Hessian forces
Hessian forces were German auxiliary troops hired by the British Crown during the American Revolutionary War, known for their disciplined fighting and prominent role in key battles such as Trenton.
F. None of above. chosen

Statements (48)

Predicate	Object
instanceOf	constrained optimization method ⓘ mathematical technique ⓘ optimization method ⓘ
appliesTo	equality constraints ⓘ finite-dimensional optimization problems ⓘ
assumes	differentiable constraint functions ⓘ differentiable objective function ⓘ
canFind	local maxima ⓘ local minima ⓘ saddle points ⓘ
classification	first-order necessary condition method ⓘ
component	Lagrange multipliers (scalars or vectors) ⓘ constraint functions ⓘ objective function ⓘ
condition	gradient of objective is linear combination of gradients of constraints ⓘ
coreIdea	convert constrained problem into unconstrained problem using auxiliary variables ⓘ
defines	Lagrangian function ⓘ
extendedTo	functional analysis ⓘ infinite-dimensional optimization ⓘ
field	mathematical optimization ⓘ multivariable calculus ⓘ nonlinear programming ⓘ
generalizedBy	Karush–Kuhn–Tucker conditions ⓘ
geometricInterpretation	level sets of objective tangent to constraint surface at optimum ⓘ
historicalPeriod	18th century ⓘ
introduces	Lagrange multiplier variables ⓘ
limitation	does not by itself distinguish maxima from minima ⓘ may find only stationary points, not necessarily global extrema ⓘ
mathematicalFormulation	stationary points of the Lagrangian satisfy gradient conditions ⓘ
namedAfter	Joseph-Louis Lagrange ⓘ
relatedTo	KKT conditions ⓘ Lagrangian mechanics ⓘ dual optimization problems ⓘ method of undetermined coefficients ⓘ saddle points of the Lagrangian ⓘ
requires	regularity conditions on constraints ⓘ
typicalAssumption	constraints define a smooth manifold ⓘ
usedFor	constrained optimization problems ⓘ finding extrema of functions with equality constraints ⓘ maximization under constraints ⓘ minimization under constraints ⓘ
usedIn	control theory ⓘ economics ⓘ engineering design ⓘ machine learning ⓘ operations research ⓘ physics ⓘ variational calculus ⓘ

How these facts were elicited

Referenced by (7)

Full triples — surface form annotated when it differs from this entity's canonical label.

Joseph-Louis Lagrange → knownFor → Lagrange multipliers ⓘ

Karush–Kuhn–Tucker conditions → relatedTo → Lagrange duality ⓘ

linked to: Lagrange multipliers

Lagrangian function → relatedTo → Lagrange multipliers ⓘ

Ramsey pricing → usesTool → Lagrange multipliers ⓘ

Support Vector Machine → usesConcept → Lagrange multipliers ⓘ

subject linked to: Support Vector Machines

Fritz John conditions → involves → Lagrange multipliers ⓘ

Fritz John conditions → relatedTo → Lagrange multiplier rule ⓘ