Function Minimization and Automatic Differentiation Using C++

Abstract

Function minimization techniques often require values for the first partial derivatives of the function at a point. Certain techniques, such as Newton's method, require the values of the second partial derivatives as well. The methods commonly used to obtain these values have certain drawbacks which can be eliminated using a technique known as automatic differentiation. When this technique is implemented in an object oriented language with operator overloading capabilities, the problem of differentiation and minimization can be mapped into a code which fits well with the problem space.