Modeling, Computation and Optimization.

By: Bapat, R. BContributor(s): Neogy, S. K | Das, A. KMaterial type: TextTextSeries: Statistical Science and Interdisciplinary Research SerPublisher: Singapore : World Scientific Publishing Co Pte Ltd, 2009Copyright date: ©2009Description: 1 online resource (348 pages)Content type: text Media type: computer Carrier type: online resourceISBN: 9789814273510Subject(s): Decision making -- Mathematical models | Mathematical models | Mathematical optimization | Numerical analysisGenre/Form: Electronic books.Additional physical formats: Print version:: Modeling, Computation and OptimizationDDC classification: 511.8 LOC classification: QA401.M5365 2009Online resources: Click to View
Contents:
Contents -- Foreword -- Preface -- Acknowledgments -- 1. Modeling a Jamming Game for Wireless Networks Andrey Garnaev -- Abstract -- Key Words -- 1.1 Introduction -- 1.2 The Main Results -- 1.3 Conclusion -- Bibliography -- 2. Existence of Nash Networks in the One-way Flow Model of Network Formation J. Derks, J. Kuipers, M. Tennekes and F. Thuijsman -- Abstract -- Key Words -- 2.1 Introduction -- 2.2 Model and Notations -- 2.3 Owner-homogeneous Costs -- 2.4 Heterogeneous Costs -- 2.5 Strict Nash Networks -- Bibliography -- 3. Strategic Advertisement with Externalities: A New Dynamic Approach Reinoud Joosten -- Abstract -- Key Words -- 3.1 Introduction -- 3.2 The Rules of the Game -- 3.2.1 Immediate Effects, Stage Games -- 3.2.2 Long Term Effects, Market Potentials -- 3.2.3 Combining Immediate and Long Term Effects -- 3.3 What Can They Do, What Can They Get? -- 3.4 What is 'Rational' to Do? -- 3.5 Pareto Efficiency -- 3.6 Conclusion -- 3.7 Appendix -- Bibliography -- 4. Connections between Some Concepts in Reliability and Economics Subhash Kochar and Maochao Xu -- Abstract -- Key Words -- 4.1 Introduction -- 4.2 Transforms from Economics and Reliability -- 4.3 Partial Orders in Economics and Reliability -- 4.4 Relative Aging Orders -- Acknowledgements -- Bibliography -- 5. A New Axiomatization of the Shapley Value for TUgames in terms of Semi-null Players Applied to 1-concave Games Theo S.H. Driessen -- Abstract -- Key Words -- 5.1 Introductory Notions -- 5.2 The Classical Axiomatization of the Shapley Value Using Null Player Property -- 5.3 A New Axiomatization of the Shapley Value Using Semi-null Player Property and 1-concave Games -- 5.4 Appendix: the Proof of Theorem 5.1 -- Bibliography -- 6. Coextrema Additive Operators Atsushi Kajii, Hiroyuki Kojima and Takashi Ui -- Abstract -- KeyWords -- 6.1 Introduction.
6.2 The Model and Preliminary Results -- 6.3 Coextrema Additive Operators -- 6.4 Main Characterization Result -- 6.5 The Proof -- Acknowledgements -- Bibliography -- 7. Models without Main Players T. S. Arthanari -- Abstract -- Key Words -- 7.1 Introduction -- 7.2 The Key Drivers of Economic Growth -- 7.3 Elimination of Main Player in Language and in Action -- 7.4 Revelation- Models without Main Players -- 7.4.1 Need for the Paradigm Shift -- 7.5 On the Ubiquitous Applications of Game Theory -- 7.6 Game Engineering -- 7.7 Beating the System According to Ackoff and Rovin -- 7.7.1 Beating The System - Examples -- 7.8 Nature of Creativity -- 7.9 Conclusions -- Acknowledgements -- Bibliography -- 8. Dynamic Optimal Advertising Expenditure Strategies for Two Successive Generations of High Technology Products Udayan Chanda and A. K. Bardhan -- Abstract -- Key Words -- 8.1 Introduction -- 8.2 Literature Review -- 8.3 Model Formulation -- 8.3.1 A Subclass of the General Formulation -- 8.4 Special Functional Form -- 8.4.1 Optimal Advertisement Expenditure Strategies -- 8.5 Conclusions -- Acknowledgements -- Appendix -- Bibliography -- 9. Nonconvex Vector Minimization with Set Inclusion Constraint Anjana Gupta, Aparna Mehra and Davinder Bhatia -- Abstract -- Key Words -- 9.1 Introduction -- 9.2 Nonlinear Scalarization -- 9.3 Sufficient Optimality Criteria -- 9.4 Necessary Optimality Criteria -- 9.5 Duality -- 9.6 Concluding Remarks -- Acknowledgements -- Bibliography -- 10. Approximate Optimality in Semi Infinite Programming Deepali Gupta and Aparna Mehra -- Abstract -- Key Words -- 10.1 Introduction -- 10.2 Approximate Solution -- 10.3 Approximate Optimality Conditions -- 10.4 Bounded KKT Multipliers -- 10.5 Concluding Remarks -- Acknowledgements -- Bibliography.
11. A Relaxation Based Solution Approach for the Inventory Control and Vehicle Routing Problem in Vendor Managed Systems Oguz Solyali and Haldun Sural -- Abstract -- Key Words -- 11.1 Introduction -- 11.2 Problem Definition and Formulation -- 11.3 Lagrangian Relaxation Based Solution Approach -- 11.3.1 Lower Bounding Procedure -- Supplier's Order Problem (ORDER) -- Supplier's Inventory Problem (SINV ) -- Distribution Problem (DIST) -- Retailers' Replenishment Problem (RET) -- 11.3.2 Upper Bounding Procedure -- 11.3.3 Solution of the Lagrangian Dual Problem -- 11.4 Computational Experiments -- 11.4.1 Small Instances -- 11.4.2 Large Instances -- 11.5 Conclusions -- Bibliography -- 12. The Distribution of Deficit at Ruin on a Renewal Risk Model K. K. Thampi and M. J. Jacob -- Abstract -- Key Words -- 12.1 Introduction -- 12.2 Ruin Probability (u) -- 12.3 Severity of Ruin -- 12.4 Different Claim Amount Distributions -- 12.4.1 Exponential Distribution -- 12.4.2 Gamma Distribution -- 12.4.3 Mixed Exponential Distribution -- 12.4.4 Generalized Exponential Distribution -- Acknowledgements -- Bibliography -- 13. Fair Allocations to Discourage Free Riding Behavior Kim Hang Pham Do and Henk Folmer -- Abstract -- Key Words -- 13.1 Introduction -- 13.2 Notation and Preliminaries -- 13.3 Feasible Allocations -- 13.4 Applications -- 13.4.1 The Baltic Sea cod fishery -- 13.4.2 The Norwegian spring-spawning herring fishery -- 13.5 Concluding Remarks -- Bibliography -- 14. A Stackelberg Di erential Game with Overlapping Generations for the Management of a Renewable Resource Luca Grilli -- Abstract -- Key Words -- 14.1 Introduction -- 14.2 Differential Game and Overlapping Generations -- 14.3 The Leader-Follower Approach -- 14.3.1 The Model -- 14.3.2 Remarks -- 14.4 Conclusions -- Bibliography.
15. Benders' Partitioning Approach for Solving the Optimal Communication Spanning Tree Problem Yogesh K. Agarwal and Prabha Sharma -- Abstract -- Key Words -- 15.1 Introduction and Problem Definition -- 15.2 Literature Review -- 15.3 A Brief Overview of the Benders' Partitioning Approach -- 15.4 Applying Benders' Partitioning to OCSTP -- 15.4.1 Computation of the Dual Solution -- 15.4.2 Computation of the Benders' Cut -- 15.4.3 The Benders' Master Problem and the Solution Approach -- 15.5 Neighborhood Search Heuristic for OCSTP -- 15.5.1 Implementation Issues -- 15.6 Neighborhood Search Using Benders' Partitioning Approach -- 15.6.1 Computational Issues Pertaining to Implementation of HB -- 15.6.2 Computational Enhancements in Implementation of HB -- 15.7 Computational Experiments and Results -- 15.7.1 A Methodology for Performance Comparison of Local Search Heuristics with Random Restart -- 15.8 Computational Results -- 15.9 Concluding Remarks -- Bibliography -- 16. Sperner's Lemma with Multiple Labels R. B. Bapat -- Abstract -- Key Words -- 16.1 Introduction -- 16.2 Sperner's Lemma with Arbitrary Labels -- 16.3 Multiple Labels -- Bibliography -- 17. Incremental Twin Support Vector Machines Reshma Khemchandani, Jayadeva and Suresh Chandra -- Abstract -- Key Words -- 17.1 Introduction -- 17.2 Twin Support Vector Machines -- 17.3 Training Incremental Twin Support Vector Machines -- 17.4 Experimental Results -- 17.5 Concluding Remarks -- Acknowledgements -- Bibliography -- 18. Portfolio Risk Management Using Support Vector Machine Sanjeet Singh -- Abstract -- Key Words -- 18.1 Introduction -- 18.2 Portfolio Risk Management -- 18.3 Support Vector Machine -- 18.3.1 Linearly or Non-linearly Separable SVM -- 18.3.2 The Linear Separable Case -- 18.3.3 The Linear Non-separable Case -- 18.3.4 Multi-class SVMs -- 18.4 Experimental Results -- 18.5 Conclusion.
Acknowledgements -- Bibliography -- 19. Weak Convergence of an Iterative Scheme with aWeaker Coe cient Condition Yasunori Kimura -- Abstract -- KeyWords -- 19.1 Introduction -- 19.2 Preliminaries -- 19.3 Weak Convergence of an Iterative Scheme under the Opial Property -- 19.4 Weak Convergence of an Iterative Scheme under the Frechet Differentiability of the Norm -- 19.5 Iterative Scheme for a Single m-accretive Operator -- Acknowledgements -- Bibliography -- 20. Complementarity Modeling and Game Theory: A Survey S. K. Neogy and A. K. Das -- Abstract -- Key Words -- 20.1 Introduction -- 20.2 Various Complementarity Problems and its Algorithms -- 20.2.1 Linear Complementarity Problem -- 20.2.2 Vertical Linear Complementarity Problem -- 20.2.3 Extended Linear Complementarity Problem -- 20.2.4 Lemke's Algorithm -- 20.2.5 Cottle-Dantzig Algorithm for Vertical Linear Complementarity Problem -- 20.3 Complementarity Models for Bimatrix Games, Polymatrix Games and its Generalizations -- 20.3.1 Bimatrix Games -- 20.3.2 Generalized Bimatrix Game -- 20.3.3 Polymatrix Games -- 20.3.4 Generalized Polymatrix Game -- 20.3.5 Complementarity Model Associated with a Generalized Polymatrix Game -- 20.4 Complementarity Models in Stochastic Games -- 20.4.1 Discounted Switching Controller Stochastic Games -- 20.4.2 Undiscounted Switching Controller Game -- 20.4.3 Discounted Zero-sum Stochastic Game with Additive Reward and Additive Transition -- 20.4.4 Undiscounted Zero-Sum Stochastic Game with Additive Reward and Additive Transition -- 20.4.5 Mixture Class of Stochastic Game -- 20.5 Concluding Remarks and Areas of Further Research -- Bibliography.
Summary: Key Features:Brings together topics like modeling, computation and optimizationContains a timely overview of research trendsIncludes a balanced mixture of theory and applicationsServes as an essential resource for current work in mathematical modeling, computations, optimization and their applications.
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Contents -- Foreword -- Preface -- Acknowledgments -- 1. Modeling a Jamming Game for Wireless Networks Andrey Garnaev -- Abstract -- Key Words -- 1.1 Introduction -- 1.2 The Main Results -- 1.3 Conclusion -- Bibliography -- 2. Existence of Nash Networks in the One-way Flow Model of Network Formation J. Derks, J. Kuipers, M. Tennekes and F. Thuijsman -- Abstract -- Key Words -- 2.1 Introduction -- 2.2 Model and Notations -- 2.3 Owner-homogeneous Costs -- 2.4 Heterogeneous Costs -- 2.5 Strict Nash Networks -- Bibliography -- 3. Strategic Advertisement with Externalities: A New Dynamic Approach Reinoud Joosten -- Abstract -- Key Words -- 3.1 Introduction -- 3.2 The Rules of the Game -- 3.2.1 Immediate Effects, Stage Games -- 3.2.2 Long Term Effects, Market Potentials -- 3.2.3 Combining Immediate and Long Term Effects -- 3.3 What Can They Do, What Can They Get? -- 3.4 What is 'Rational' to Do? -- 3.5 Pareto Efficiency -- 3.6 Conclusion -- 3.7 Appendix -- Bibliography -- 4. Connections between Some Concepts in Reliability and Economics Subhash Kochar and Maochao Xu -- Abstract -- Key Words -- 4.1 Introduction -- 4.2 Transforms from Economics and Reliability -- 4.3 Partial Orders in Economics and Reliability -- 4.4 Relative Aging Orders -- Acknowledgements -- Bibliography -- 5. A New Axiomatization of the Shapley Value for TUgames in terms of Semi-null Players Applied to 1-concave Games Theo S.H. Driessen -- Abstract -- Key Words -- 5.1 Introductory Notions -- 5.2 The Classical Axiomatization of the Shapley Value Using Null Player Property -- 5.3 A New Axiomatization of the Shapley Value Using Semi-null Player Property and 1-concave Games -- 5.4 Appendix: the Proof of Theorem 5.1 -- Bibliography -- 6. Coextrema Additive Operators Atsushi Kajii, Hiroyuki Kojima and Takashi Ui -- Abstract -- KeyWords -- 6.1 Introduction.

6.2 The Model and Preliminary Results -- 6.3 Coextrema Additive Operators -- 6.4 Main Characterization Result -- 6.5 The Proof -- Acknowledgements -- Bibliography -- 7. Models without Main Players T. S. Arthanari -- Abstract -- Key Words -- 7.1 Introduction -- 7.2 The Key Drivers of Economic Growth -- 7.3 Elimination of Main Player in Language and in Action -- 7.4 Revelation- Models without Main Players -- 7.4.1 Need for the Paradigm Shift -- 7.5 On the Ubiquitous Applications of Game Theory -- 7.6 Game Engineering -- 7.7 Beating the System According to Ackoff and Rovin -- 7.7.1 Beating The System - Examples -- 7.8 Nature of Creativity -- 7.9 Conclusions -- Acknowledgements -- Bibliography -- 8. Dynamic Optimal Advertising Expenditure Strategies for Two Successive Generations of High Technology Products Udayan Chanda and A. K. Bardhan -- Abstract -- Key Words -- 8.1 Introduction -- 8.2 Literature Review -- 8.3 Model Formulation -- 8.3.1 A Subclass of the General Formulation -- 8.4 Special Functional Form -- 8.4.1 Optimal Advertisement Expenditure Strategies -- 8.5 Conclusions -- Acknowledgements -- Appendix -- Bibliography -- 9. Nonconvex Vector Minimization with Set Inclusion Constraint Anjana Gupta, Aparna Mehra and Davinder Bhatia -- Abstract -- Key Words -- 9.1 Introduction -- 9.2 Nonlinear Scalarization -- 9.3 Sufficient Optimality Criteria -- 9.4 Necessary Optimality Criteria -- 9.5 Duality -- 9.6 Concluding Remarks -- Acknowledgements -- Bibliography -- 10. Approximate Optimality in Semi Infinite Programming Deepali Gupta and Aparna Mehra -- Abstract -- Key Words -- 10.1 Introduction -- 10.2 Approximate Solution -- 10.3 Approximate Optimality Conditions -- 10.4 Bounded KKT Multipliers -- 10.5 Concluding Remarks -- Acknowledgements -- Bibliography.

11. A Relaxation Based Solution Approach for the Inventory Control and Vehicle Routing Problem in Vendor Managed Systems Oguz Solyali and Haldun Sural -- Abstract -- Key Words -- 11.1 Introduction -- 11.2 Problem Definition and Formulation -- 11.3 Lagrangian Relaxation Based Solution Approach -- 11.3.1 Lower Bounding Procedure -- Supplier's Order Problem (ORDER) -- Supplier's Inventory Problem (SINV ) -- Distribution Problem (DIST) -- Retailers' Replenishment Problem (RET) -- 11.3.2 Upper Bounding Procedure -- 11.3.3 Solution of the Lagrangian Dual Problem -- 11.4 Computational Experiments -- 11.4.1 Small Instances -- 11.4.2 Large Instances -- 11.5 Conclusions -- Bibliography -- 12. The Distribution of Deficit at Ruin on a Renewal Risk Model K. K. Thampi and M. J. Jacob -- Abstract -- Key Words -- 12.1 Introduction -- 12.2 Ruin Probability (u) -- 12.3 Severity of Ruin -- 12.4 Different Claim Amount Distributions -- 12.4.1 Exponential Distribution -- 12.4.2 Gamma Distribution -- 12.4.3 Mixed Exponential Distribution -- 12.4.4 Generalized Exponential Distribution -- Acknowledgements -- Bibliography -- 13. Fair Allocations to Discourage Free Riding Behavior Kim Hang Pham Do and Henk Folmer -- Abstract -- Key Words -- 13.1 Introduction -- 13.2 Notation and Preliminaries -- 13.3 Feasible Allocations -- 13.4 Applications -- 13.4.1 The Baltic Sea cod fishery -- 13.4.2 The Norwegian spring-spawning herring fishery -- 13.5 Concluding Remarks -- Bibliography -- 14. A Stackelberg Di erential Game with Overlapping Generations for the Management of a Renewable Resource Luca Grilli -- Abstract -- Key Words -- 14.1 Introduction -- 14.2 Differential Game and Overlapping Generations -- 14.3 The Leader-Follower Approach -- 14.3.1 The Model -- 14.3.2 Remarks -- 14.4 Conclusions -- Bibliography.

15. Benders' Partitioning Approach for Solving the Optimal Communication Spanning Tree Problem Yogesh K. Agarwal and Prabha Sharma -- Abstract -- Key Words -- 15.1 Introduction and Problem Definition -- 15.2 Literature Review -- 15.3 A Brief Overview of the Benders' Partitioning Approach -- 15.4 Applying Benders' Partitioning to OCSTP -- 15.4.1 Computation of the Dual Solution -- 15.4.2 Computation of the Benders' Cut -- 15.4.3 The Benders' Master Problem and the Solution Approach -- 15.5 Neighborhood Search Heuristic for OCSTP -- 15.5.1 Implementation Issues -- 15.6 Neighborhood Search Using Benders' Partitioning Approach -- 15.6.1 Computational Issues Pertaining to Implementation of HB -- 15.6.2 Computational Enhancements in Implementation of HB -- 15.7 Computational Experiments and Results -- 15.7.1 A Methodology for Performance Comparison of Local Search Heuristics with Random Restart -- 15.8 Computational Results -- 15.9 Concluding Remarks -- Bibliography -- 16. Sperner's Lemma with Multiple Labels R. B. Bapat -- Abstract -- Key Words -- 16.1 Introduction -- 16.2 Sperner's Lemma with Arbitrary Labels -- 16.3 Multiple Labels -- Bibliography -- 17. Incremental Twin Support Vector Machines Reshma Khemchandani, Jayadeva and Suresh Chandra -- Abstract -- Key Words -- 17.1 Introduction -- 17.2 Twin Support Vector Machines -- 17.3 Training Incremental Twin Support Vector Machines -- 17.4 Experimental Results -- 17.5 Concluding Remarks -- Acknowledgements -- Bibliography -- 18. Portfolio Risk Management Using Support Vector Machine Sanjeet Singh -- Abstract -- Key Words -- 18.1 Introduction -- 18.2 Portfolio Risk Management -- 18.3 Support Vector Machine -- 18.3.1 Linearly or Non-linearly Separable SVM -- 18.3.2 The Linear Separable Case -- 18.3.3 The Linear Non-separable Case -- 18.3.4 Multi-class SVMs -- 18.4 Experimental Results -- 18.5 Conclusion.

Acknowledgements -- Bibliography -- 19. Weak Convergence of an Iterative Scheme with aWeaker Coe cient Condition Yasunori Kimura -- Abstract -- KeyWords -- 19.1 Introduction -- 19.2 Preliminaries -- 19.3 Weak Convergence of an Iterative Scheme under the Opial Property -- 19.4 Weak Convergence of an Iterative Scheme under the Frechet Differentiability of the Norm -- 19.5 Iterative Scheme for a Single m-accretive Operator -- Acknowledgements -- Bibliography -- 20. Complementarity Modeling and Game Theory: A Survey S. K. Neogy and A. K. Das -- Abstract -- Key Words -- 20.1 Introduction -- 20.2 Various Complementarity Problems and its Algorithms -- 20.2.1 Linear Complementarity Problem -- 20.2.2 Vertical Linear Complementarity Problem -- 20.2.3 Extended Linear Complementarity Problem -- 20.2.4 Lemke's Algorithm -- 20.2.5 Cottle-Dantzig Algorithm for Vertical Linear Complementarity Problem -- 20.3 Complementarity Models for Bimatrix Games, Polymatrix Games and its Generalizations -- 20.3.1 Bimatrix Games -- 20.3.2 Generalized Bimatrix Game -- 20.3.3 Polymatrix Games -- 20.3.4 Generalized Polymatrix Game -- 20.3.5 Complementarity Model Associated with a Generalized Polymatrix Game -- 20.4 Complementarity Models in Stochastic Games -- 20.4.1 Discounted Switching Controller Stochastic Games -- 20.4.2 Undiscounted Switching Controller Game -- 20.4.3 Discounted Zero-sum Stochastic Game with Additive Reward and Additive Transition -- 20.4.4 Undiscounted Zero-Sum Stochastic Game with Additive Reward and Additive Transition -- 20.4.5 Mixture Class of Stochastic Game -- 20.5 Concluding Remarks and Areas of Further Research -- Bibliography.

Key Features:Brings together topics like modeling, computation and optimizationContains a timely overview of research trendsIncludes a balanced mixture of theory and applicationsServes as an essential resource for current work in mathematical modeling, computations, optimization and their applications.

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Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2018. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.

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