J. Stoer - Böcker

Mathematics is playing an ever more important role in the physical and biological sciences, provoking a blurring of boundaries between scientific disciplines and a resurgence of interest in the modern as well as the classical techniques of applied mathematics. This renewal of interest, both in re­ search and teaching, has led to the establishment of the series Texts in Applied Mathematics (TAM). The development of new courses is a natural consequence of a high level of excitement on the research frontier as newer techniques, such as numeri­ cal and symbolic computer systems, dynamical systems, and chaos, mix with and reinforce the traditional methods of applied mathematics. Thus, the purpose of this textbook series is to meet the current and future needs of these advances and to encourage the teaching of new courses. TAM will publish textbooks suitable for use in advanced undergraduate and beginning graduate courses, and will complement the Applied Mathe­ matical Sciences (AMS) series, which will focus on advanced textbooks and research-level monographs.

Mathematics is playing an ever more important role in the physical and biological sciences, provoking a blurring of boundaries between scientific disciplines and a resurgence of interest in the modern as well as the classical techniques of applied mathematics.

The book of Professor Evtushenko describes both the theoretical foundations and the range of applications of many important methods for solving nonlinear programs. Particularly emphasized is their use for the solution of optimal control problems for ordinary differential equations. These methods were instrumented in a library of programs for an interactive system (DISO) at the Computing Center of the USSR Academy of Sciences, which can be used to solve a given complicated problem by a combination of appropriate methods in the interactive mode. Many examples show the strong as well the weak points of particular methods and illustrate the advantages gained by their combination. In fact, it is the central aim of the author to pOint out the necessity of using many techniques interactively, in order to solve more dif­ ficult problems. A noteworthy feature of the book for the Western reader is the frequently unorthodox analysis of many known methods in the great tradition of Russian mathematics. J. Stoer PREFACE Optimization methods are finding ever broader application in sci­ ence and engineering. Design engineers, automation and control systems specialists, physicists processing experimental data, eco­ nomists, as well as operations research specialists are beginning to employ them routinely in their work. The applications have in turn furthered vigorous development of computational techniques and engendered new directions of research. Practical implementa­ tion of many numerical methods of high computational complexity is now possible with the availability of high-speed large-memory digital computers.

The book is devoted to a simplified set-theoretic version of denotational semantics where sets are used in place of Scott's reflexive domains and where jumps are described without continuations. This approach has emerged as a reaction to the sophisticated model of traditional semantics. It was also strongly stimulated by the applications of denotational semantics and especially by its software-industry oriented version known as VDM (Vienna Development Method). The new approach was successfully tested on several examples. Based on this approach the Polish Academy of Sciences created the project MetaSoft aimed at the development of a definitional metalanguage for software engineering. The approach has also been chosen in the project RAISE (ESPRIT) which aims at a similar goal. The book consists of two parts. Part One is devoted to the mathematical foundations of the future definitional metalanguage of MetaSoft. This part also introduces an appropriate notation. Part Two shows the applications of this metalanguage. There the denotational definition of a subset of Pascal is discussed with particular emphasis on Pascal types.