Numerical Methods of Optimization

Jean-Pierre Corriou
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Jean-Pierre Corriou: University of Lorraine

Chapter Chapter 9 in Numerical Methods and Optimization, 2021, pp 505-574 from Springer

Abstract: Abstract The numerical methods of optimization start with optimizing functions of one variable, bisection, Fibonacci, and Newton. Then, functions of several variables occupy the main part, divided into methods of direct search and gradient methods. In the direct search, many methods are presented, simplex, Hooke and Jeeves, Powell, Rosenbrock, Nelder–Mead, Box complex, genetic algorithms with quasi-global optimization. Gradient methods are first explained from a general point of view for quadratic and non-quadratic functions, including the method of steepest descent, conjugate gradients, Newton–Raphson, quasi-Newton, Gauss–Newton, and Levenberg–Marquardt. Solving large systems is discussed. All these methods are illustrated by significant numerical examples.

Date: 2021
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DOI: 10.1007/978-3-030-89366-8_9

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