Mathematical Programming and Game Theory for Decision Making.
Title:
Mathematical Programming and Game Theory for Decision Making.
Author:
Neogy, S. K.
ISBN:
9789812813220
Personal Author:
Physical Description:
1 online resource (500 pages)
Series:
Statistical Science and Interdisciplinary Research ; v.1
Statistical Science and Interdisciplinary Research
Contents:
Contents -- Foreword -- Preface -- Acknowledgments -- 1. Mathematical Programming and its Applications in Finance L. C. Thomas -- Abstract -- 1.1 Introduction -- 1.2 Portfolio Optimization -- 1.3 Asset-liability Models -- 1.4 Yield Curves -- 1.5 Credit Scorecards -- Bibliography -- 2. Anti-stalling Pivot Rule for Linear Programs with Totally Unimodular Coe cient Matrix S. N. Kabadi and A. P. Punnen -- Abstract -- 2.1 Introduction -- 2.2 Pivot Selection Rule -- Bibliography -- 3. A New Practically E cient Interior Point Method for Convex Quadratic Programming K. G. Murty -- Abstract -- 3.1 Introduction -- 3.2 The Centering Strategy -- 3.3 Descent Step Using a Descent Direction -- 3.4 Descent Step Using the Touching Constraints -- 3.5 The Algorithm -- 3.6 Convergence Results -- 3.7 The Case When the Matrix D is Not Positive Definite -- Bibliography -- 4. A General Framework for the Analysis of Sets of Constraints R. Caron and T. Traynor -- Abstract -- 4.1 Introduction -- 4.2 The Set Covering Formulation -- 4.3 Random Sampling -- Acknowledgement -- Bibliography -- 5. Tolerance-based Algorithms for the Traveling Salesman Problem D. Ghosh, B. Goldengorin, G. Gutin and G. J ager -- Abstract -- 5.1 Introduction -- 5.2 Some Relevant Concepts -- 5.2.1 The Relaxed Assignment Problem -- 5.2.2 Determining Tolerances for AP and RAP -- 5.2.3 The Contraction Procedure and a Greedy Algorithm -- 5.3 Tolerance-based Greedy Algorithms -- 5.4 Computational Experience -- 5.5 Summary and Future Research Directions -- Bibliography -- 6. On the Membership Problem of the Pedigree Polytope T. S. Arthanari -- Abstract -- 6.1 Introduction -- 6.1.1 Computational Complexity, Polytopes and Efficiency -- 6.2 Preliminaries & Notations -- 6.2.1 Rigid, Dummy arcs in a Capacited Transportation Problem -- 6.2.2 Definition of the Pedigree Polytope.
6.2.3 Multistage Insertion and Related Results -- 6.3 Polytopes and Efficiency -- 6.3.0.1 Problems Related to Polytopes -- 6.3.1 Properties of the Polytope, conv(An) -- 6.4 Construction of the Layered Network N -- 6.5 Necessity of Fk Feasibility for Membership -- 6.6 Pedigree Packability -- 6.7 A Multicommodity Flow Problem to Check Member- ship -- 6.8 Computational Complexity of Checking the Necessary Condition -- 6.9 Concluding Remarks -- Acknowledgements -- Bibliography -- 7. Exact Algorithms for a One-defective Vertex Colouring Problem N. Achuthan, N. R. Achuthan and R. Collinson -- Abstract -- 7.1 Introduction -- 7.2 Sequential Colouring Heuristics for k-DVCP -- 7.3 Implicit Enumeration Algorithms for 1-DVCP -- 7.4 Computational Performance of the Algorithms -- Acknowledgement -- Bibliography -- 8. Complementarity Problem involving a Vertical Block Matrix and its Solution using Neural Network Model S. K. Neogy, A. K. Das and P. Das -- Abstract -- 8.1 Introduction -- 8.2 Preliminaries -- 8.3 Main Results -- 8.4 Computing VLCP Solution Using the Neural Network Dynamics -- 8.4.1 Proposed Neural Network Dynamics -- 8.5 Simulation Results -- Bibliography -- 9. Fuzzy Twin Support Vector Machines for Pattern Classi cation R. Khemchandani, Jayadeva and S. Chandra -- Abstract -- 9.1 Introduction -- 9.2 Support Vector Machines -- 9.3 Twin Support Vector Machines -- 9.4 Fuzzy Twin Support Vector Machines -- 9.5 Experimental Results -- 9.6 Concluding Remarks -- Acknowledgements -- Bibliography -- 10. An Overview of the Minimum Sum of Absolute Errors Regression S. C. Narula and J. F. Wellington -- Abstract -- 10.1 Introduction -- 10.2 Computational Algorithms -- 10.3 Statistical Properties and Inference -- 10.4 Variable Selection -- 10.5 Coefficient of Determination -- 10.6 Other Results -- 10.7 Likelihood Displacement -- 10.8 Robustness.
10.9 Multiple Criteria Linear Regression Using MSAE -- 10.10 Concluding Remarks -- Bibliography -- 11. Hedging against the Market with No Short Selling S. A. Clark and C. Srinivasan -- Abstract -- 11.1 Introduction -- 11.2 Securities Market Model -- 11.3 Fundamental Value -- 11.4 Trading Strategies -- 11.5 Hedging Prices -- Bibliography -- 12. Mathematical Programming and Electrical Network Analysis II: Computational Linear Algebra through Network analysis H. Narayanan -- Abstract -- 12.1 Introduction -- 12.2 Electrical Network Analysis Procedures -- 12.2.1 Nodal Analysis -- 12.2.2 Loop Analysis -- 12.2.3 Hybrid Analysis -- 12.3 Experimental Results -- 12.4 A Proposal -- 12.5 Conclusion -- Appendix: A variation of PCG -- A.1 Modi ed CG -- A.2 Modi ed Preconditioned CG -- A.3 Justi cation for Modi ed Preconditioned CG -- Bibliography -- 13. Dynamic Optimal Control Policy in Price and Quality for High Technology Product A. K. Bardhan and U. Chanda -- Abstract -- 13.1 Introduction -- 13.2 Dynamic Diffusion of Demand -- 13.3 Model Development -- 13.4 Dynamic Optimization -- 13.5 Theoretical Results -- 13.6 Pricing and Quality Impact on Leapfrogging -- 13.7 Optimal Introduction Timing Strategy for Second Generation Product -- 13.8 Conclusions -- Acknowledgement -- Appendix -- A. Optimal Pricing -- B. Significance of Pricing and Quality in Leapfrogging -- C. Optimal Introduction Timing Strategy -- Bibliography -- 14. Forecasting for Supply Chain and Portfolio Management K. G. Murty -- Abstract -- 14.1 Introduction -- 14.2 Costs of High Inventories and Shortages -- 14.3 Commonly used Techniques for Forecasting Demand -- 14.4 Parametric Methods for Forecasting Demand Distri- bution -- 14.4.1 Using Normal Distribution with updating of Ex- pected Value and Standard Deviation in each Period.
14.4.2 Using Normal Distribution with Updating of Ex- pected Value and Standard Deviation only when there is Evidence of Change -- 14.4.3 Using Distributions other than Normal -- 14.5 A Nonparametric Method for Updating and Forecast- ing the Entire Demand Distribution -- 14.6 An Application of the Forecasting Method of Section 14.5 for computing Optimal Order Quantities -- 14.7 How to incorporate Seasonality in Demand into the Model -- 14.8 Portfolio Management -- 14.9 Variance as a Measure of Risk, and the Markovitz Model for Portfolio Optimization -- 14.10 Other Measures of Risk for Portfolio Optimization -- 14.11 Portfolio Management: Tracking the Distribution of Return from a Portfolio that is kept for a Long Time -- 14.12 A Model based on Statistical Learning to nd an Op- timum Portfolio -- Bibliography -- 15. Variational Analysis in Bilevel Programming S. Dempe, J. Dutta and B. S. Mordukhovich -- Abstract -- 15.1 Introduction -- 15.2 Tools from Variational Analysis -- 15.3 Partially Convex Lower-level Problems -- 15.4 Fully Convex Lower-level Problems -- Acknowledgements -- 16. Game Engineering R. J. Aumann -- Auctions: -- Bibliography -- Arbitration: -- Traffic: -- 17. Games of Connectivity P. Dubey and R. Garg -- Abstract -- 17.1 Introduction -- 17.2 Examples -- 17.2.1 Multicast Transmission -- 17.2.2 Unicast Transmission -- 17.2.3 Transmission of Layered Information -- 17.2.4 Transmission of Information Partitions -- 17.2.5 General Network with Controlled Edges -- 17.3 The Abstract Model -- 17.3.1 The Communications Network -- 17.3.2 Information -- 17.3.3 Location of Players and Public Facilities -- 17.3.4 Control of Edges -- 17.3.5 The Transmission of Information -- 17.3.6 The Reception of Information -- 17.3.7 The Cost of a Transmission -- 17.3.8 The Bene t from a Transmission -- 17.4 The Connectivity Game.
17.5 The Growing Transmissions Property -- 17.6 Remarks -- 17.7 Appendix -- 17.7.1 Proof of Theorem 17.1 -- 17.7.2 Proof of Theorem 17.2 -- Bibliography -- 18. A Robust Feedback Nash Equilibrium in a Climate Change Policy Game M. Hennlock -- Abstract -- 18.1 Introduction -- 18.2 The Climate Models -- 18.2.1 Climate Change Impacts -- 18.3 Players and Payo s -- 18.3.1 Investor i 2 [1 -- n] -- 18.3.2 Policy Maker j 2 [1 -- N] -- 18.3.3 Game Formulations -- 18.4 Concluding Comments -- 18.5 Summary -- 18.6 Appendix -- 18.6.1 Appendix A.1 Proof of Proposition 1 -- 18.6.2 Appendix A.2 Proof of Proposition 2 -- Bibliography -- 19. De Facto Delegation and Proposer Rules H. Imai and K. Yonezaki -- Abstract -- 19.1 Introduction -- 19.2 Model and Result -- 19.3 Proof -- 19.4 FO rule and Discussion -- 19.5 Conclusion -- Acknowledgements -- Bibliography -- 20. The Bargaining Set in E ectivity Function D. Raza mahatolotra -- 20.1 Introduction -- 20.2 Definitions and Notations -- 20.3 Some Analysis of Cycles -- 20.4 Stability and Cycles -- 20.4.1 Comparison of the Bargaining Sets -- 20.4.2 The Zhou's Bargaining Set -- 20.4.3 The Mass-Colell's Bargaining Set -- 20.5 Annexe -- Bibliography -- 21. Dynamic Oligopoly as a Mixed Large Game { Toy Market A. Wiszniewska-Matyszkiel -- Abstract -- 21.1 Introduction -- 21.1.1 Large Games -- 21.2 Formulation of the Basic Model -- 21.2.1 Producers -- 21.2.2 Parents (and Children) -- 21.2.3 Market Clearing -- 21.3 Results -- 21.3.1 Case A: Two Periods with Dead-Season -- 21.3.2 Case B: Two Periods -- 21.3.3 Case C: Finitely Many Stages and Negligibility of Low Advertising Efforts -- 21.3.4 Case D: In nite Time Horizon and Negligibility of Low Advertising Efforts -- 21.4 Conclusions -- Bibliography -- 22. On Some Classes of Balanced Games R. B. Bapat -- Abstract -- 22.1 Introduction -- 22.2 Regression Games.
22.3 Connectivity Games.
Abstract:
This edited book presents recent developments and state-of-the-art review in various areas of mathematical programming and game theory. It is a peer-reviewed research monograph under the ISI Platinum Jubilee Series on Statistical Science and Interdisciplinary Research. This volume provides a panoramic view of theory and the applications of the methods of mathematical programming to problems in statistics, finance, games and electrical networks. It also provides an important as well as timely overview of research trends and focuses on the exciting areas like support vector machines, bilevel programming, interior point method for convex quadratic programming, cooperative games, non-cooperative games and stochastic games. Researchers, professionals and advanced graduates will find the book an essential resource for current work in mathematical programming, game theory and their applications. Sample Chapter(s). Foreword (45 KB). Chapter 1: Mathematical Programming and its Applications in Finance (177 KB). Contents: Mathematical Programming and Its Applications in Finance (L C Thomas); Anti-Stalling Pivot Rule for Linear Programs with Totally Unimodular Coefficient Matrix (S N Kabadi & A P Punnen); A New Practically Efficient Interior Point Method for Convex Quadratic Programming (K G Murty); A General Framework for the Analysis of Sets of Constraints (R Caron & T Traynor) , Tolerance-Based Algorithms for the Traveling Salesman Problem (D Ghosh et al.); On the Membership Problem of the Pedigree Polytope (T S Arthanari); Exact Algorithms for a One-Defective Vertex Colouring Problem (N Achuthan et al.); Complementarity Problem Involving a Vertical Block Matrix and Its Solution Using Neural Network Model (S K Neogy et al.); Fuzzy Twin Support Vector Machines for Pattern Classification (R Khemchandani et al.); An Overview of the Minimum Sum of Absolute
Errors Regression (S C Narula & J F Wellington); Hedging Against the Market with No Short Selling (S A Clark & C Srinivasan); Mathematical Programming and Electrical Network Analysis II: Computational Linear Algebra Through Network Analysis (H Narayanan); Dynamic Optimal Control Policy in Price and Quality for High Technology Product (A K Bardhan & U Chanda); Forecasting for Supply Chain and Portfolio Management (K G Murty); Variational Analysis in Bilevel Programming (S Dempe et al.); Game Engineering (R J Aumann); Games of Connectivity (P Dubey & R Garg); A Robust Feedback Nash Equilibrium in a Climate Change Policy Game (M Hennlock); De Facto Delegation and Proposer Rules (H Imai & K Yonezaki); The Bargaining Set in Effectivity Function (D Razafimahatolotra); Dynamic Oligopoly as a Mixed Large Game - Toy Market (A Wiszniewska-Matyszkiel); On Some Classes of Balanced Games (R B Bapat); Market Equilibrium for Combinatorial Auctions and the Matching Core of Nonnegative TU Games (S Lahiri); Continuity, Manifolds, and Arrow's Social Choice Problem (K Saukkonen); On a Mixture Class of Stochastic Games with Ordered Field Property (S K Neogy). Readership: Researchers, professionals and advanced students in mathematical programming, game theory, management sciences and computational mathematics.
Local Note:
Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2017. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.
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