In this section we outline some basic techniques involving deterministic algorithms for finding local minima of multivariate functions whose arguments are continuous and on which no restrictions are imposed. For constrained problems, techniques are based on those for unconstrained problems, and we mention only general approaches to them at the end of this section. It should be emphasized that finding the global minimum is an entirely different, and more challenging, problem which will not be addressed here. Basically, stochastic methods are better suited at this time for large-scale global optimization (see Figure 4) and some appropriate algorithms will be outlined in Section 4.
Figure 4: The Structure of Local and Global Minimization Algorithms.