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Nonlinear Equations and Optimization

In: Dynamic General Equilibrium Modeling

Author

Listed:
  • Burkhard Heer

    (University of Augsburg)

  • Alfred Maußner

    (University of Augsburg)

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.

Suggested Citation

  • Burkhard Heer & Alfred Maußner, 2024. "Nonlinear Equations and Optimization," Springer Texts in Business and Economics, in: Dynamic General Equilibrium Modeling, edition 3, chapter 0, pages 811-846, Springer.
    • Handle: RePEc:spr:sptchp:978-3-031-51681-8_15
    DOI: 10.1007/978-3-031-51681-8_15
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