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 5.
For comprehensive presentations on deterministic optimization techniques for multivariate functions, we refer the reader to excellent textbooks , some recent volumes and reviews . The outline in this section is not intended to provide full algorithmic details of all available methods; rather it exposes key algorithmic concepts and modules, so that the reader could consult specialized literature for further details. Further background details can also be obtained from the linear algebra chapter.