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1 results

  • 6 - Numerical Minimization Process

  • from Part II - Practical Tools
  • Seon Ki Park, Milija Zupanski, Colorado State University
  • Book:
    Principles of Data Assimilation
    Published online:
    22 September 2022
    Print publication:
    29 September 2022, pp 128-160

  • Summary

    Mathematical background and formulation of numerical minimization process are described in terms of gradient-based methods, whose ingredients include gradient, Hessian, directional derivatives, optimality conditions for minimization, Hessian eigensystem, conjugate number of Hessian, and conjugate vectors. Various minimization algorithms, such as the steepest descent method, Newton’s method, conjugate gradient method, and quasi-Newton’s method, are introduced along with practical examples.