Minimization
Abstract
Variational data assimilation of satellite observations must solve minimization problems of extremely large dimensions for which only the values of the cost function and its gradient can be evaluated, but not its Hessian matrix. The minimum of the cost function is obtained using an iterative, unconstrained minimization algorithm. Selected materials in minimization are provided in this chapter for readers to gain some basic understanding of minimization software, how to use them wisely, and how to modify them if needed. Starting with the basic concepts of the optimality conditions of functionals and cost functions, important concepts of line search and search direction are first introduced. Mathematical methods of ...
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