Optimization theory优化理论

2004-7  

化学工业出版社  

Jongen, H. Th; Jongen, Hubertus; Meer, Klaus  

443  

　　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.

PrefaceI Continuous Optimization1 Optimality Criteria on Simple Regions2 Constraints, Lagrange Function, Optimality3 Parametric Aspects, Semi-Infinite Optimization4 Convex Functions, Duality, Separation Theorem5 Linear Inequalities, Constraint Qualifications6 Linear Programming: The Simplex Method7 The Ellipsoid Method8 Karmarkar's Method for Linear Programming9 Order of Convergence, Steepest Descent10 Conjugate Direction, Variable Metric11 Penalty-, Barrier-, Multiplier-, IP-Methods12 Search Methods without Derivatives13 One-Dimensional MinimizationII Discrete Optimization14 Graphs and Networks15 Flows in Networks16 Applications of the Max-Flow Min-Cut Theorem17 Integer Linear Programming18 Computability; the Turing machine19 Complexity theory20 Reducibility and NP-completeness21 Some NP-completeness results22 The Random Access Machine23 Complexity Theory over the Real Numbers24 Approximating NP-hard Problems25 Approximation Algorithms for TSP26 Approximation algorithms for Bin Packing27 A FPTAS for Knapsack28 MiscellaneousIndexIndex of SymbolsReferences

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