Nonlinear Equations and Optimization

Burkhard Heer and Alfred Maußner ()
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Alfred Maußner: University of Augsburg

Chapter Chapter 15 in Dynamic General Equilibrium Modeling, 2024, pp 811-846 from Springer

Abstract: Abstract This chapter presents numerical methods used to locate the roots of systems of nonlinear equations or find the extrema of real-valued functions defined on a subset of Euclidean n-space. It demonstrates the close link between the two kinds of problem, since the solution of a root-finding problem can be transformed into a nonlinear minimization problem. With one exception (genetic search), the authors consider algorithms that are iterative, proceeding from a given initial point in successive steps. First, they develop stopping criteria for the iterative algorithms. Next, they consider standard methods used to solve nonlinear equations including the (modified) Newton-Raphson and Gauss-Seidel methods, before describing numerical optimization methods such as the golden section search, Newton’s method, and quasi Newton methods.

Date: 2024
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DOI: 10.1007/978-3-031-51681-8_15

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