Continuous problems: optimality, complexity, tractability

Since a digital computer is able to store and manipulate only with finitely many real numbers, most computational problems of continuous mathematics can only be solved approximately using partial information. A branch of computational mathematics that studies the inherent difficulty of continuous problems, for which available information is partial, noisy, and priced, is called information-based complexity (IBC). IBC emerged as a branch of computational mathematics some 30 years ago as a consequence of the need to study theoretical aspects of computations related to continuous problems. Since then IBC developed in different directions, see, e.g., the monographs [1, 2, 6, 7, 8, 9, 10, 11]. In IBC study, an important role, both theoretical and practical, play problems that are defined on functions of many or even infinitely many variables. In physical or chemical applications, the number o