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."

New edition of a well-known classic in the field; Previous edition sold over 6000 copies worldwide; Fully-worked examples; Many carefully selected problems

This book contains a large amount of information not found in standard textbooks. Written for the advanced undergraduate/beginning graduate student, it combines the modern mathematical standards of numerical analysis with an understanding of the needs of the computer scientist working on practical applications. Among its many particular features are: fully worked-out examples; many carefully selected and formulated problems; fast Fourier transform methods; a thorough discussion of some important minimization methods; solution of stiff or implicit ordinary differential equations and of differential algebraic systems; modern shooting techniques for solving two-point boundary value problems; and basics of multigrid methods. This new edition features expanded presentation of Hermite interpolation and B-splines, with a new section on multi-resolution methods and B-splines. New material on differential equations and the iterative solution of linear equations include: solving differential equations in the presence of discontinuities whose locations are not known at the outset; techniques for sensitivity analyses of differential equations dependent on additional parameters; new advanced techniques in multiple shooting; and Krylov space methods for non-symmetric systems of linear equations.