Applied Mathematical Sciences

Optimization

Algorithms and Consistent Approximations

Editors: Polak, Elijah (Ed.)

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About this book

This book deals with optimality conditions, algorithms, and discretization tech­ niques for nonlinear programming, semi-infinite optimization, and optimal con­ trol problems. The unifying thread in the presentation consists of an abstract theory, within which optimality conditions are expressed in the form of zeros of optimality junctions, algorithms are characterized by point-to-set iteration maps, and all the numerical approximations required in the solution of semi-infinite optimization and optimal control problems are treated within the context of con­ sistent approximations and algorithm implementation techniques. Traditionally, necessary optimality conditions for optimization problems are presented in Lagrange, F. John, or Karush-Kuhn-Tucker multiplier forms, with gradients used for smooth problems and subgradients for nonsmooth prob­ lems. We present these classical optimality conditions and show that they are satisfied at a point if and only if this point is a zero of an upper semicontinuous optimality junction. The use of optimality functions has several advantages. First, optimality functions can be used in an abstract study of optimization algo­ rithms. Second, many optimization algorithms can be shown to use search directions that are obtained in evaluating optimality functions, thus establishing a clear relationship between optimality conditions and algorithms. Third, estab­ lishing optimality conditions for highly complex problems, such as optimal con­ trol problems with control and trajectory constraints, is much easier in terms of optimality functions than in the classical manner. In addition, the relationship between optimality conditions for finite-dimensional problems and semi-infinite optimization and optimal control problems becomes transparent.

Table of contents (5 chapters)

Table of contents (5 chapters)

Buy this book

eBook $229.00
price for USA in USD (gross)
  • ISBN 978-1-4612-0663-7
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $289.00
price for USA in USD
  • ISBN 978-0-387-94971-0
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $159.99
price for USA in USD
  • ISBN 978-1-4612-6861-1
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Optimization
Book Subtitle
Algorithms and Consistent Approximations
Editors
  • Elijah Polak
Series Title
Applied Mathematical Sciences
Series Volume
124
Copyright
1997
Publisher
Springer-Verlag New York
Copyright Holder
Springer-Verlag New York, Inc.
eBook ISBN
978-1-4612-0663-7
DOI
10.1007/978-1-4612-0663-7
Hardcover ISBN
978-0-387-94971-0
Softcover ISBN
978-1-4612-6861-1
Series ISSN
0066-5452
Edition Number
1
Number of Pages
XX, 782
Topics