Optimization Techniques: An Introduction - Softcover

Inhaltsangabe

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.

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