Maximum

You are given a function in n-dimensional space,

Which might have a lot of arguments.

You know that this function has a physical sense,

You should maximize it subject to given constraints.

 

Refrain

 

You will take the derivative

For any choice of the cost functional

And you will find the maximum

You’ve been searching for a long-long time.

 

If constraints are specified

On the set of admissible arguments,

Then just write the Lagrangian

And find zeroes of its gradient.

 

 

 

You know that in any maximum point

The derivative has a zero value

But you need to check that the Hessian

Is negative definite, you’ll do it, you can.

 

Refrain.

 

 

The gradient method requires to compute

The gradient value, and it will be so cute.

And Newton needs to linearize,

Then the speed of convergence will substantially rise.

 

Refrain.