The new framework can be treated as a hybrid approach between global and local methods. It differs from traditional local methods by computing multiple local solutions in the neighborhood region in a systematic manner. It differs from global methods by working completely in the profile space and searching a subspace efficiently in a deterministic manner. For a given non-convex function, there is a massive number of convergence regions that are very close to each other and are separated from one another in the form of different basins of attraction. These basins are effectively modeled by the concept of stability regions.