Optimization Theory

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Springer Science & Business Media, Jul 20, 2004 - Computers - 443 pages
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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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Contents

16
13
Constraints Lagrange Function Optimality
19
22
33
Parametric Aspects SemiInfinite Optimization
34
Convex Functions Duality Separation Theorem
49
II
63
Linear Inequalities Constraint Qualifications
66
The Simplex Method
81
Approximation algorithms for Bin Packing
375
A FPTAS for Knapsack
383
28
391
Index
409
242
410
248
413
257
414
35
415

14
191
Applications of the MaxFlow MinCut Theorem
236
The GaleRyserTheorem 16 2 Königs Theorem 16 3 Dilworths Theorem 16 4 Mengers Theorem 16 5 The Minimum Cost Flow Problem Integer Line...
257
Totally unimodular matrices Unimodularity and integer linear programming Integral polyhedra Computability the Turing machine
271
19
282
23
297
Running time the class P Some important decision problems 19 3 19 4 Nondeterministic Turing machines The class NP Reducibility and NPcomplete...
301
Polynomial time reductions NPcompleteness Cooks theorem A polynomial time algorithm for 2SAT Some NPcompleteness results
312
The Random Access Machine
329
Complexity Theory over the Real Numbers
333
viii
353
Approximation Algorithms for
364
273
416
283
417
294
419
303
423
55
428
304
429
329
430
95
434
349
436
191
441
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