Introduction

First equation

Lagrange Multiplier Example

Setting equations 1 and 2 equal to each other

Plugging in y squared

Example 4

Isolating y

Conclusion

Intro

How to solve the system of equations

Filling in the Equations

Deriving the partial derivative of H with respect to y

Finding the multipliers

Plugging values into constraints

Plugging in Values

Using the Second Mu Value

Plugging in maximum and minimum values

Maximum and minimum

Introduction

Lagrange Polynomials

The Lagrange Interpolation formula

The Resulting Polynomials

Intro

Lagrange Polynomials

Visualizing L2

Numeric Example

Example Visualized

Why Lagrange Works

Lagrange Accuracy

Error

Error Visualized

Error Bounds

Notes

Thanks For Watching

Recap

Twin Stereo Spacecraft

Earth-Sun Lagrange Point

Wind Spacecraft

Planck Space Observatory

Spektar-RG

ESA's Euclid

ESA's Planned L2 Missions

Earth-Moon Lagrange Point

Patreon shout outs

Generalized variables and equations of motion

Kinetic energy equation

Potential energy equation

Potential energy of second spring

Applying the Lagrangian to the system

Equations of motion

Using partial derivatives

Finding partial derivative of lagrangian with respect to x2

Conclusion

Intro

Lagrangian function and duality

Lagrangian dual function

Lower bound on the optimal value

MATLAB: Lower bound verification

Example 1 - Least Squares

Example 2 - Linear Programming

Example 3 - Two-way Partitioning

Relationship between conjugate function and the dual function

Example 4 - Equality Constrained Norm minimization

Example 5 - Entropy Maximization

Outro