Optimization theory优化理论
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作者： Hubertus Th. Jongen, Klaus Meer, Eberhard Triesch著
出 版 社： 化学工业出版社
出版时间： 2004-7-1字数：版次： 1页数： 443印刷时间： 2004/07/01开本： 16开印次： 1纸张： 胶版纸I S B N ： 9781402080982包装： 精装内容简介
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.
目录
Preface
I Continuous Optimization
1 Optimality Criteria on Simple Regions
2 Constraints, Lagrange Function, Optimality
3 Parametric Aspects, Semi-Infinite Optimization
4 Convex Functions, Duality, Separation Theorem
5 Linear Inequalities, Constraint Qualifications
6 Linear Programming: The Simplex Method
7 The Ellipsoid Method
8 Karmarkar's Method for Linear Programming
9 Order of Convergence, Steepest Descent
10 Conjugate Direction, Variable Metric
11 Penalty-, Barrier-, Multiplier-, IP-Methods
12 Search Methods without Derivatives
13 One-Dimensional Minimization
II Discrete Optimization
14 Graphs and Networks
15 Flows in Networks
16 Applications of the Max-Flow Min-Cut Theorem
17 Integer Linear Programming
18 Computability; the Turing machine
19 Complexity theory
20 Reducibility and NP-completeness
21 Some NP-completeness results
22 The Random Access Machine
23 Complexity Theory over the Real Numbers
24 Approximating NP-hard Problems
25 Approximation Algorithms for TSP
26 Approximation algorithms for Bin Packing
27 A FPTAS for Knapsack
28 Miscellaneous
Index
Index of Symbols
References