CUSTOMIZING METHODS FOR GLOBAL OPTIMIZATION - A GEOMETRIC VIEWPOINT

A new class of global optimization algorithms, extending the multidimensional bisection method of Wood, is described geometrically. New results show how the geometry of the global minimum relates to performance. Remarkably, the epigraph of the objective function, turned upside down, plays a key role. Algorithms customized to take advantage of special information about the objective function belong to the class. A number of algorithms in the literature, including those of Piyavskii-Shubert, Mladineo, Wood and Breiman & Cutler, also belong, and simple modifications of them produce customized algorithms. Comparison of various algorithms in the class is provided.