An Introduction to Optimisation and the Solution of Nonlinear Equations

This chapter discusses a number of robust nonlinear solvers for univariate functions based on C++11 and the Boost C++ libraries. Next, it details how and why the algorithms work. Also, these algorithms work with a variety of function types in C++ in combination with input arguments and associated parameters. The mathematical and numerical entities are mapped into software components. Having addressed software design issues, the chapter integrates the numerical algorithms into a software framework based on the system decomposition techniques. The methods and techniques from the chapter can be applied to the construction of software libraries and frameworks in numerical analysis applications such as interpolation and numerical quadrature. Furthermore, the chapter examines the twin topics of computing the roots of functions and function minimisation and subsequent implementation in C++. Finally, it discusses the important topic of how to compute implied volatility.