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商品描述
Theory of Linear and Integer Programming Alexander Schrijver Centrum voor Wiskunde en Informatica, Amsterdam, The Netherlands This book describes the theory of linear and integer programming and surveys the algorithms for linear and integer programming problems, focusing on complexity analysis. It aims at complementing the more practically oriented books in this field. A special feature is the authora s coverage of important recent developments in linear and integer programming. Applications to combinatorial optimization are given, and the author also includes extensive historical surveys and bibliographies. The book is intended for graduate students and researchers in operations research, mathematics and computer science. It will also be of interest to mathematical historians. Contents 1 Introduction and preliminaries; 2 Problems, algorithms, and complexity; 3 Linear algebra and complexity; 4 Theory of lattices and linear diophantine equations; 5 Algorithms for linear diophantine equations; 6 Diophantine approximation and basis reduction; 7 Fundamental concepts and results on polyhedra, linear inequalities, and linear programming; 8 The structure of polyhedra; 9 Polarity, and blocking and anti--blocking polyhedra; 10 Sizes and the theoretical complexity of linear inequalities and linear programming; 11 The simplex method; 12 Primal--dual, elimination, and relaxation methods; 13 Khachiyana s method for linear programming; 14 The ellipsoid method for polyhedra more generally; 15 Further polynomiality results in linear programming; 16 Introduction to integer linear programming; 17 Estimates in integer linear programming; 18 The complexity of integer linear programming; 19 Totally unimodular matrices: fundamental properties and examples; 20 Recognizing total unimodularity; 21 Further theory related to total unimodularity; 22 Integral polyhedra and total dual integrality; 23 Cutting planes; 24 Further methods in integer linear programming; Historical and further notes on integer linear programming; References; Notation index; Author index; Subject index
商品描述(中文翻譯)
線性與整數規劃理論
亞歷山大·施瑞佛
阿姆斯特丹數學與計算機科學中心，荷蘭
本書描述了線性與整數規劃的理論，並調查了線性與整數規劃問題的算法，重點在於複雜度分析。它旨在補充該領域中更具實用導向的書籍。書中一個特別的特色是作者對線性與整數規劃中重要的近期發展的涵蓋。書中提供了對組合優化的應用，並且作者還包括了廣泛的歷史調查和參考文獻。本書適合運籌學、數學和計算機科學的研究生和研究人員，也將引起數學歷史學家的興趣。
內容
1 引言與初步知識；
2 問題、算法與複雜度；
3 線性代數與複雜度；
4 格理論與線性迪奧芬方程的理論；
5 線性迪奧芬方程的算法；
6 迪奧芬近似與基底縮減；
7 多面體、線性不等式與線性規劃的基本概念與結果；
8 多面體的結構；
9 極性、阻塞與反阻塞多面體；
10 線性不等式與線性規劃的大小與理論複雜度；
11 單純形法；
12 原始-對偶、消去與放鬆方法；
13 Khachiyan 的線性規劃方法；
14 更一般的多面體橢圓法；
15 線性規劃中的進一步多項式結果；
16 整數線性規劃簡介；
17 整數線性規劃中的估計；
18 整數線性規劃的複雜度；
19 完全單模矩陣：基本性質與例子；
20 辨識完全單模性；
21 與完全單模性相關的進一步理論；
22 整數多面體與完全對偶整數性；
23 切割平面；
24 整數線性規劃中的進一步方法；
整數線性規劃的歷史與進一步說明；
參考文獻；
符號索引；
作者索引；
主題索引。
