Optimization Theory / Edition 1

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Optimization Theory is becoming a more and more important mathematical as well as interdisciplinary area, especially in the interplay between mathematics and many other sciences like computer science, physics, engineering, operations research, etc. This volume gives a comprehensive introduction into the theory of (deterministic) optimization on an advanced undergraduate and graduate level. One main feature is the treatment of both continuous and discrete optimization at the same place. This allows to study the problems under different points of view, supporting a better understanding of the entire field. Audience: The book can be adapted well as an introductory textbook into optimization theory on a basis of a two semester course; however, each of its parts can also be taught separately. Many exercises are included to increase the reader's understanding.

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Editorial Reviews

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"If you have to read a book about (deterministic) optimization in finite dimension, this is the one. The book covers the whole theory of modern optimization; the authors have included a lot of exercises, examples and figures that make the book understandable and more interesting. All the current knowledge on existence of solutions, optimality criteria, structural properties of the models as well as the algorithms … have been included in this work in a rigorous, concise and elegant manner." (Francisco Guerra Vazquez, Zentralblatt MATH, Vol. 1059 (10), 2005)

"The book covers a wide range of subjects pertaining to mathematical programming … . The various subjects are described in considerable detail, several examples are given and numerous examples problems are proposed. The authors write that the book is intended for undergraduates and graduates, but I think that it might be useful also for those postgraduates who wish to learn the basic aspects of mathematical programming … . The book has a rich list of bibliographical references which are surely useful … ." (Giorgio Giorgi, Mathematical Reviews, Issue 2005 b)

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Product Details

  • ISBN-13: 9781402080982
  • Publisher: Springer US
  • Publication date: 7/20/2004
  • Edition description: 2004
  • Edition number: 1
  • Pages: 456
  • Product dimensions: 9.21 (w) x 6.14 (h) x 1.00 (d)

Table of Contents

I Continuous optimization 1
1 Optimality criteria on simple regions 3
2 Constraints, Lagrange function, optimality 19
3 Parametric aspects, semi-infinite optimization 35
4 Convex functions, duality, separation theorem 49
5 Linear inequalities, constraint qualifications 67
6 Linear programming : the simplex method 81
7 The ellipsoid method 97
8 Karmarkar's method for linear programming 113
9 Order of convergence, steepest descent 125
10 Conjugate direction, variable metric 141
11 Penalty-, barrier-, multiplier-, IP-methods 153
12 Search methods without derivatives 173
13 One-dimensional minimization 183
II Discrete optimization 191
14 Graphs and networks 193
15 Flows in networks 227
16 Applications of the max-flow min-cut theorem 239
17 Integer linear programming 257
18 Computability; the Turing machine 271
19 Complexity theory 283
20 Reducibility and NP-completeness 301
21 Some NP-completeness results 313
22 The random access machine 329
23 Complexity theory over the real numbers 333
24 Approximating NP-hard problems 353
25 Approximation algorithms for TSP 365
26 Approximation algorithms for bin packing 375
27 A FPTAS for knapsack 383
28 Miscellaneous 391
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