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Numerical Methods and Optimization in Finance by Enrico Schumann, Dietmar Maringer, Manfred Gilli

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Chapter Eleven

Basic Methods

Publisher Summary

This chapter is about classic methods for unconstrained optimization, including the special case of nonlinear least squares. Optimization is also related to finding the zeros of a function; thus, the solution of nonlinear systems of equations is also part of this chapter. A variety of approaches are considered, depending on whether one is in a one-dimensional setting or one solves problems in higher dimensions. The choice of a particular method may depend on the application. For instance, the method of bisection needs an interval and may, therefore, be considered more robust. It can be noted that for finding the roots of a polynomial, there exist specific algorithms, which resort to the computation ...

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