* Lambda denotes a Lagrange multiplier in multi-dimensional calculus.

* The Lagrange multiplier mathematical technique

We introduce a new variable () called a Lagrange multiplier and study the Lagrange function defined by

Thus, the force on a particle due to a scalar potential,, can be interpreted as a Lagrange multiplier determining the change in action ( transfer of potential to kinetic energy ) following a variation in the particle's constrained trajectory.

Moreover, by the envelope theorem the optimal value of a Lagrange multiplier has an interpretation as the marginal effect of the corresponding constraint constant upon the optimal attainable value of the original objective function: if we denote values at the optimum with an asterisk, then it can be shown that

For example, in economics the optimal profit to a player is calculated subject to a constrained space of actions, where a Lagrange multiplier is the change in the optimal value of the objective function due to the relaxation of a given constraint ( e. g. through a change in income ); in such a context is the marginal cost of the constraint, and is referred to as the shadow price.

The Lagrange multiplier has an economic interpretation as the shadow price associated with the constraint, in this example the marginal utility of income.

# REDIRECT Lagrange multiplier

where is a Lagrange multiplier.

where the Lagrange multiplier is a non-negative constant that establishes the appropriate balance between rate and distortion.

Each link capacity imposes a constraint, which gives rise to a Lagrange multiplier,.

* Lagrange multiplier, a method for finding maxima and minima subject to constraints

the additional parameter is a Lagrange multiplier used in the minimization of the kriging error to honor the unbiasedness condition.

When the probability is derived from the Gibbs measure, as it would be for any Markovian process, then can also be understood to be a Lagrange multiplier ; Lagrange multipliers are used to enforce constraints, such as holding the expectation value of some quantity constant.

A methodology to test for the lag length of ARCH errors using the Lagrange multiplier test was proposed by Engle ( 1982 ).

This is done by a Lagrange multiplier technique.

The constraints on the system dynamics can be adjoined to the Lagrangian by introducing time-varying Lagrange multiplier vector, whose elements are called the costates of the system.

Pontryagin's minimum principle states that the optimal state trajectory, optimal control, and corresponding Lagrange multiplier vector must minimize the Hamiltonian so that

We can then formulate the problem using a Lagrange multiplier:

where is the Einstein-Hilbert action, and is the lapse function ( i. e., the Lagrange multiplier for the Hamiltonian constraint ).

# REDIRECT Lagrange multiplier

This problem may be solved using the Lagrange multiplier technique to yield the optimal output values, and backing out the optimal prices.

If the generalized coordinates are represented as a vector and time differentiation is represented by a dot over the variable, then the equations of motion ( known as the Lagrange or Euler – Lagrange equations ) are a set of equations:

In addition to the original (" primal ") variable we introduce a Lagrange multiplier inspired dual variable ( sometimes called " slack variable ")

There is a special case of Lagrange inversion theorem that is used in combinatorics and applies when and Take to obtain We have

Around 1770, Joseph Louis Lagrange began the groundwork that unified the many different tricks that had been used up to that point to solve equations, relating them to the theory of groups of permutations, in the form of Lagrange resolvents.

* Conceptual introduction ( plus a brief discussion of Lagrange multipliers in the calculus of variations as used in physics )

The STScI is currently developing similar processes for JWST, although the operational details will be very different due to its different instrumentation and spacecraft constraints, and its location at the Sun-Earth L2 Lagrange point (~ 1. 5 million km from Earth ) rather than the low Earth orbit (~ 565 km ) used by HST.

Although generalized to triple integrals by Lagrange in 1773, and used by Legendre, Laplace, Gauss, and first generalized to n variables by Mikhail Ostrogradski in 1836, it resisted a fully rigorous formal proof for a surprisingly long time, and was first satisfactorily resolved 125 years later, by Élie Cartan in a series of papers beginning in the mid-1890s (; ).

Although Lagrange only sought to describe classical mechanics, the action principle that is used to derive the Lagrange equation was later recognized to be applicable to quantum mechanics as well.

In numerical analysis, Lagrange polynomials are used for polynomial interpolation.

Lagrange polynomials are used in the Newton – Cotes method of numerical integration and in Shamir's secret sharing scheme in cryptography.

The identity was used by Lagrange to prove his four square theorem.

** Konami VRC7, used in one Famicom game Lagrange Point.

Jumps are normally made to and from points far above a solar system's ecliptic, usually where the gravitational influence in the system is most stable ; however, so-called " pirate points " exist where local gravitational pull is stable enough to used ; though quicker, using such points is also more dangerous due the random appearance of so-called " Lagrange points ".

Whereas optimization methods are nearly as old as calculus, dating back to Isaac Newton, Leonhard Euler, Daniel Bernoulli, and Joseph Louis Lagrange, who used them to solve problems such as the shape of the catenary curve, numerical optimization reached prominence in the digital age.

Constraints can be used explicitly by the solution algorithm or can be incorporated into the objective using Lagrange multipliers.

In spaceflight, especially for NASA's Constellation Program, the term sortie has been used for a flight of the Orion spacecraft beyond the confluence of low-Earth orbit, such as a flight to the Moon or to the Sun-Earth L < sub > 2 </ sub > Lagrange Point.

Lagrange first used the method in 1766.

* Konami's VRC7 soundchip is a YM2413 derivative, used exclusively on the NES game Lagrange Point.

Lagrange Point has the distinction of being the only game ever released with Konami's VRC7 sound generator Integrated Circuit, which allowed for a drastic improvement in the quality of the music and sound effects used in the game.

* Games used in: Lagrange Point, Tiny Toon Adventures 2

This advanced audio was used only in the Famicom game Lagrange Point ; while the Japanese version of Tiny Toon Adventures 2 also used the VRC7, it did not make use of the extended audio.