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Chapman and Hall Mathematics Series

Mathematical Programming and Control Theory

Authors: Craven, B. D.

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eBook $84.99
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  • ISBN 978-94-009-5796-1
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Softcover $109.99
price for USA in USD
  • ISBN 978-0-412-15500-0
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About this book

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.

Table of contents (7 chapters)

Table of contents (7 chapters)

Buy this book

eBook $84.99
price for USA in USD
  • ISBN 978-94-009-5796-1
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $109.99
price for USA in USD
  • ISBN 978-0-412-15500-0
  • Free shipping for individuals worldwide
  • Institutional customers should get in touch with their account manager
  • Covid-19 shipping restrictions
  • Usually ready to be dispatched within 3 to 5 business days, if in stock
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Bibliographic Information

Bibliographic Information
Book Title
Mathematical Programming and Control Theory
Authors
Series Title
Chapman and Hall Mathematics Series
Copyright
1978
Publisher
Springer Netherlands
Copyright Holder
B. D. Craven
eBook ISBN
978-94-009-5796-1
DOI
10.1007/978-94-009-5796-1
Softcover ISBN
978-0-412-15500-0
Edition Number
1
Number of Pages
XII, 164
Topics