Chapter IX Global optimization

Publisher Summary This chapter focuses on global optimization. The problem of designing algorithms that distinguish between the local optima and locate the best possible one is known as the “global optimization problem.” Any method for global optimization has to account for the fact that a numerical procedure can never produce more than approximate answers. Irrespective of whether a global optimization method is deterministic or stochastic, it always aims for an appropriate convergence guarantee. A natural approach to solve the global optimization problem is through an appropriate generalization of branch and bound methods. A deterministic approach can be shown to be optimal in the worst case sense, whereas a stochastic approach can be shown to be optimal in the expected utility sense, but neither method can be recommended unless evaluations of the original function f are very expensive. Global optimization as a research area is still on its way to maturity. The variety of techniques proposed is impressive, but their relative merits have neither been analyzed in a systematic manner nor properly investigated in computational experiments.