The
fundamental structure of local iterative techniques for solving
unconstrained minimization problems is simple. A starting point is
chosen; a direction of movement is prescribed according to some
algorithm, and a *line search* or *trust region*
approach is performed
to determine an appropriate next step. The process is repeated at
the new point and the algorithm continues until a local minimum is
found (see Figure 5).
Schematically, a model local minimizer method can be
sketched as follows:

Figure 5 The Structure of a Line-Search Based Local Minimization Algorithm. View Figure

(See exercise 1.)

- 2.2.1 Descent Directions
- 2.2.2 Line Search and Trust Region Steps
- 2.2.3 Convergence Criteria
- 2.2.4 Convergence Characterization