Information-based Complexity and Information-based Optimization

This is an article that will appear in the Encyclopedia of Optimization (Kluwer, 2000). It concerns optimization in two senses. The first is that informaion-based complexity (IBC) is the study of the minimal computational resources to solve continuous mathematical problems. The second is that the computational complexity of optimization problems is one of the areas studied in IBC. We discuss IBC and information-based optimization in turn. This article concerns optimization in two senses. The first is that information-based complexity (IBC) is the study of the minimal computational resources to solve continuous mathematical problems. (Other types of mathematical problems are also studied; the problems studied by IBC will be characterized later.) J.F. Traub and A.G. Werschulz [14] provide an expository introduction to the theory and applications of IBC, with over 400 recent papers and books. A general formulation with proofs can be found in J.F. Traub, G.W. Wasilkowski, and H. Woźniakowski [13]. The second is that the computational complexity of optimization problems is one of the areas studied in IBC. S.A. Vavasis [16, pg. 135] calls this information-based optimization. We will discuss information-based complexity and information-based optimization in turn.