Lebesgue Measure & Integral

Science & Math

Craven, B.D.

Mathematics

Pitman Publishing

<p>In a mathematical programming problem, an optimum (maxi mum or minimum) of a function is sought, subject to con straints on the values of the variables. In the quarter century since G. B. Dantzig introduced the simplex method for linear programming, many real-world problems have been modelled in mathematical programming terms. Such problems often arise in economic planning - such as scheduling industrial production or transportation - but various other problems, such as the optimal control of an interplanetary rocket, are of similar kind. Often the problems involve nonlinear func tions, and so need methods more general than linear pro gramming. This book presents a unified theory of nonlinear mathe matical programming. The same methods and concepts apply equally to 'nonlinear programming' problems with a finite number of variables, and to 'optimal control' problems with e. g. a continuous curve (i. e. infinitely many variables). The underlying ideas of vector space, convex cone, and separating hyperplane are the same, whether the dimension is finite or infinite; and infinite dimension makes very little difference to the proofs. Duality theory - the various nonlinear generaliz ations of the well-known duality theorem of linear program ming - is found relevant also to optimal control, and the , PREFACE Pontryagin theory for optimal control also illuminates finite dimensional problems. The theory is simplified, and its applicability extended, by using the geometric concept of convex cones, in place of coordinate inequalities.</p>

Mathematical Programming and Control Theory (Chapman and Hall Mathematics Series)

Springer

<b>Control and Optimization</b> presents a systematic account of optimal control theory in relation to a general approach to optimization that is also applicable in other contexts. It covers a diversity of applications, incorporates a full chapter of worked examples, examines good computing methods, and explores some more recent results on sensitivity and approximation, invex functions in optimization models, and methods for nonsmooth problems.

Control and Optimization (Chapman Hall/CRC Mathematics Series)

Chapman and Hall/CRC

EX - Library book with all the usual stamps and markings. Slight shelf wear. Pages are clean and binding is tight.

Mathematical Programming and Control Theory

Chapman and Hall

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