A non-linear problem solver using automatic differentiation and penalty methods.

Automatic Differentiation

Let’s say you want to take the partial derivative of some function, and let’s call that function f. You could try to evaluate that partial derivative with a difference quotient: df/dx = (f(x + h) - f(x))/h where h is some very small number. However, this runs into the problem of finding the optimal value for h to reduce the amount of error in the calculation and requires as many operations as the number of variables you wish.


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