Nonconvex global optimization is based on global search methods which are quite different from local search procedures commonly used in classical mathematical programming. Although specific problems can be efficiently handled only by methods which take advantage of their particular structure, there are some general principles guiding global search processes. Furthermore, a general approach to low rank nonconvex problems is to transform a given problem of this class into a sequence of subproblems of low dimension, whose data are adaptively generated from those of the original problem. These subproblems of low dimension are often solved by a specialized version of some general purpose method.