Nonserial dynamic programming / Umberto Bertelè and Francesco Brioschi.

Includes bibliographical references (pages 229-232) and index.

Print version record.

Front Cover; Nonserial Dynamic Programming; Copyright Page; Table of Contents; Preface; Acknowledgments; Chapter 1. Nonserial Problems; 1.1 Introduction; 1.2 The Serial Unconstrained Problem; 1.3 A Problem in Inventory Theory; 1.4 The Nonserial Unconstrained Problem and Its Graph-Theoretical Representation; 1.5 A Problem in Pattern Recognition; 1.6 A Problem in Traffic Control; 1.7 The Parametric Unconstrained Problem; 1.8 The Constrained Problem; 1.9 Introduction to Nonserial Dynamic Programming and Plan of the Book

Chapter 2. The Elimination of Variables One by One: Description of the Procedure2.1 Introduction; 2.2 Serial Dynamic Programming; 2.3 Nonserial Dynamic Programming: The Description of the Solution of the Primary Problem; 2.4 An Example; 2.5 The Secondary Optimization Problem; 2.6 The Elimination Process; 2.7 Criterion Functions; 2.8 The Final Theorem and Other Dominance Relations among Elimination Orderings; 2.9 The Correspondence Theorem; 2.10 The Parametric Unconstrained Problem; Chapter 3. The Elimination of Variables One by One: Properties and Algorithms; 3.1 Introduction

3.2 Heuristic Algorithms3.3 Optimal Path Algorithms; 3.4 Computational Implications of the Final Theorem; 3.5 Further Dominance Relations among Elimination Orderings; 3.6 The Descendance Theorem; 3.7 The Initial Theorem; 3.8 The Separating Set Theorem; 3.9 Connections between Structure and Dimension in a Graph; 3.10 Upper and Lower Bounds to the Dimension; 3.11 A Branch and Bound Algorithm; Chapter 4. The Elimination of Variables in Blocks; 4.1 Introduction; 4.2 The Description of the Procedure for the Solution of the Primary Problem; 4.3 An Example; 4.4 The Secondary Optimization Problem

4.5 The Block Elimination Process4.6 Some General Properties; 4.7 The Final Theorem; 4.8 The Descendance, Initial, and Separating Set Theorems; 4.9 Bounds and Algorithms: Some Hints; 4.10 The Correspondence Theorem; 4.11 The Parametric Unconstrained ProbIem; 4.12 Concluding Remarks; Chapter 5. Multilevel Elimination Procedures; 5.1 Introduction; 5.2 Multilevel Elimination Procedures for the Solution of the Primary Problem; 5.3 An Example; 5.4 The Secondary Optimization Problem; 5.5 The Multilevel Elimination Process; 5.6 The Final Theorem; 5.7 Some General Properties

5.8 Heuristic Algorithms: Some Hints5.9 The Correspondence Theorem; Chapter 6. Constrained Problems; 6.1 Introduction; 6.2 A Penalty Function Approach; 6.3 The Elimination of Variables One by One: Description of the Procedure; 6.4 An Example; 6.5 The Secondary Optimization Problem; 6.6 Univocal Constraints; 6.7 An Example; 6.8 Dynamic Systems and Other Applications : The Block Diagram Representation; 6.9 An Example; 6.10 A Discussion about Possible Improvements of the Optimization Procedures in Some Special Cases; 6.11 An Allocation Problem; Appendix A: Review of Graph Theory; List of Symbols

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