Author | Foulds, L. R. author |
---|---|
Title | Optimization Techniques [electronic resource] : An Introduction / by L. R. Foulds |
Imprint | New York, NY : Springer New York, 1981 |
Connect to | http://dx.doi.org/10.1007/978-1-4613-9458-7 |
Descript | 502 p. online resource |
1 Introduction -- 1.1 Motivation for Studying Optimization, -- 1.2 The Scope of Optimization, -- 1.3 Optimization as a Branch of Mathematics -- 1.4 The History of Optimization -- 1.5 Basic Concepts of Optimization -- 2 Linear Programming -- 2.1 Introduction -- 2.2 A Simple L.P. Problem -- 2.3 The General L.P. Problem -- 2.4 The Basic Concepts of Linear Programming -- 2.5 The Simplex Algorithm -- 2.6 Duality and Postoptimal Analysis -- 2.7 Special Linear Program -- 2.8 Exercises -- 3 Advanced Linear Programming Topics -- 3.1 Efficient Computational Techniques for Large L.P. Problems -- 3.2 The Revised Simplex Method -- 3.3 The Dual Simplex Method -- 3.4 The Primal-Dual Algorithm -- 3.5 Dantzig-Wolfe Decomposition -- 3.6 Parametric Programming -- 3.7 Exercises -- 4 Integer Programming -- 4.1 A Simple Integer Programming Problem -- 4.2 Combinatorial Optimization -- 4.3 Enumerative Techniques -- 4.4 Cutting Plane Methods -- 4.5 Applications of Integer Programming -- 4.6 Exercises -- 5 Network Analysis -- 5.1 The Importance of Network Models -- 5.2 An Introduction to Graph Theory -- 5.3 The Shortest Path Problem -- 5.4 The Minimal Spanning Tree Problem -- 5.5 Flow Networks -- 5.6 Critical Path Scheduling -- 5.7 Exercises -- 6 Dynamic Programming -- 6.1 Introduction -- 6.2 A Simple D.P. Problem -- 6.3 Basic D.P. Structure -- 6.4 Multiplicative and More General Recursive Relationships -- 6.5 Continuous State Problems -- 6.6 The Direction of Computations -- 6.7 Tabular Form -- 6.8 Multi-state Variable Problems and the Limitations of D.P. -- 6.9 Exercises -- 7 Classical Optimization -- 7.1 Introduction -- 7.2 Optimization of Functions of One Variable -- 7.3 Optimization of Unconstrained Functions of Several Variables, -- 7.4 Optimization of Constrained Functions of Several Variables -- 7.5 The Calculus of Variations, 7.6 Exercises -- 8 Nonlinear Programming -- 8.1 Introduction -- 8.2 Unconstrained Optimization -- 8.3 Constrained Optimization -- 8.4 Exercises -- 9 Appendix -- 9.1 Linear Algebra -- 9.2 Basic Calculus -- 9.3 Further Reading -- References -- Solutions to Selected Exercises