The algorithms in the Optimization package that comes with base Maple 9.5 are local search methods. Local search methods use first and second derivatives to find a local extremum, iteratively producing points that improve the objective function while maintaining or approaching feasibility. The algorithms in the Global Optimization Toolbox are global search methods. Instead of using derivatives to find a local extremum, they systematically search the entire feasible region for a global extremum. Global search methods find a global extremum in optimization models that have many local extrema, and they do not rely on an initial point.