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Steepest Descent Methods

In: Modern Numerical Nonlinear Optimization

Author

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  • Neculai Andrei

    (Center for Advanced Modeling and Optimization)

Abstract

The steepest descent method was designed by Cauchy (1847) and is the simplest of the gradient methods for the optimization of general continuously differential functions in n variables. Its importance is due to the fact that it gives the fundamental ideas and concepts of all unconstrained optimization methods. It introduces a pattern common to many optimization methods. In this pattern, an iteration consists of two parts: the choice of a descent search direction dk followed at once by a line search to find a suitable stepsize αk. The search direction in the steepest descent method is exactly the negative gradient.

Suggested Citation

  • Neculai Andrei, 2022. "Steepest Descent Methods," Springer Optimization and Its Applications, in: Modern Numerical Nonlinear Optimization, chapter 3, pages 81-107, Springer.
    • Handle: RePEc:spr:spochp:978-3-031-08720-2_3
    DOI: 10.1007/978-3-031-08720-2_3
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