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Numerical Methods of Optimization

In: Numerical Methods and Optimization

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  • Jean-Pierre Corriou

    (University of Lorraine)

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.

Suggested Citation

  • Jean-Pierre Corriou, 2021. "Numerical Methods of Optimization," Springer Optimization and Its Applications, in: Numerical Methods and Optimization, chapter 0, pages 505-574, Springer.
    • Handle: RePEc:spr:spochp:978-3-030-89366-8_9
    DOI: 10.1007/978-3-030-89366-8_9
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    Cited by:

    1. Wiktor Olchowik & Jędrzej Gajek & Andrzej Michalski, 2023. "The Use of Evolutionary Algorithms in the Modelling of Diffuse Radiation in Terms of Simulating the Energy Efficiency of Photovoltaic Systems," Energies, MDPI, vol. 16(6), pages 1-32, March.
    2. Stanislav Stoykov & Ivan Kostov, 2023. "Price Competition with Differentiated Products on a Two-Dimensional Plane: The Impact of Partial Cartel on Firms’ Profits and Behavior," Games, MDPI, vol. 14(2), pages 1-25, March.

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