数学规划导论
2005-6
机械工业出版社
拉塞尔 C.沃克
546
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本书提供了利用数学规划作为工具所必需的背景知识，并讨论了与应用技术有关的数学方法。本书包含线性规划、整型规划、动态规划、经典的优化技术，在向量和矩阵运算以及非线性规划中应用符号软件包Maple，应用Maple进行曲线拟合，解决网络问题和线性规划问题，应用最优化软件包LINDO和LINGO的实例，以及TI-82和TI-92绘图计算软件的用法。 本书适合作为管理科学和运筹学等专业的教材，也可作为MBA的教材。 本书特点 ●包含利用最优化软件包LINDO和LINGO的示例。 ●介绍TI-82和TI-92绘图计算软件。 ●包含大量例题与习题，有助于加深读者对数学规划的理解。 ●提供许多目前颇具挑战性的问题的解决途径。
1. Introduction to the Problems. 1.1 Introduction 1.2 Types of problems to be considered 1.3 Sample problems 1.4 Sample problems 1.5 Summary and objectives2. Vectors and Matrices. 2.1 Introduction 2.2 Vectors 2.3 The span of a set of vectors 2.4 Matrices 2.5 Linear independence 2.6 Systems of equations 2.7 The inverse of a matrix 2.8 Summary and objectives3. Linear Programming. 3.1 Introduction 3.2 Slack Variables 3.3 The simplex algorithm 3.4 Basic feasible solutions and extreme points 3.5 Formulation examples 3.6 General constraints and variables 3.7 The dual and minimizing problems 3.8 Sensitivity analysis 3.9 summary and objectives4. Network Models. 4.1 Introduction 4.2 The transportation problem 4.3 The critical path method 4.4 Shortest path models 4.5 Minimal spanning trees 4.6 Summary and objectives5. Unconstrained Extrema. ……6. Constrained Extrema. 7. Integer Programming. 8. Introduction to Dynamic Programming. 9. Case Studies. Appendix A.Brief Introductions to LINDO and LINGO.Appendix B.A Brief Introduction to Maple. Appendix C.Introduction to Texas Instrument Calculators. Appendix D.Selected Answers and Hints. References. Index.
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