Second-Order Optimisation Methods
With the essential background information of Chapter 2 behind us, we are ready to turn our attention to specific second-order optimisation methods. The survey of multivariate second-order methods presented in this chapter is necessarily selective, with the focus on tried and tested methods that have a reputation for both speed and reliability. Two types of multivariate second-order method are considered — general methods (Section 3.3), and nonlinear least-squares methods (Section 3.4). The former are suitable for finding a minimum of any smooth nonlinear function F(x k ); the latter are suitable only when F(x k )is of the special form given by (1.5).
KeywordsLine Search Conjugate Gradient Method Newton Step Steep Descent Direction Exact Line Search
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