Linear Programming: Mathematics, Theory and Algorithms by M.J. Panik (English) P

Description: Linear Programming: Mathematics, Theory and Algorithms by M.J. Panik Linear Programming provides an in-depth look at simplex based as well as the more recent interior point techniques for solving linear programming problems. FORMAT Paperback LANGUAGE English CONDITION Brand New Publisher Description Linear Programming provides an in-depth look at simplex based as well as the more recent interior point techniques for solving linear programming problems. Starting with a review of the mathematical underpinnings of these approaches, the text provides details of the primal and dual simplex methods with the primal-dual, composite, and steepest edge simplex algorithms. This then is followed by a discussion of interior point techniques, including projective and affine potential reduction, primal and dual affine scaling, and path following algorithms. Also covered is the theory and solution of the linear complementarity problem using both the complementary pivot algorithm and interior point routines. A feature of the book is its early and extensive development and use of duality theory. Audience: The book is written for students in the areas of mathematics, economics, engineering and management science, and professionals who need a sound foundation in the important and dynamic discipline of linear programming. Table of Contents 1. Introduction and Overview.- 2. Preliminary Mathematics.- 2.1 Vectors in Rn.- 2.2 Rank and Linear Transformations.- 2.3 The Solution Set of a System of Simultaneous Linear Equations.- 2.4 Orthogonal Projections and Least Squares Solutions.- 2.5 Point-Set Theory: Topological Properties of Rn.- 2.6 Hyperplanes and Half-Planes (-Spaces).- 2.7 Convex Sets.- 2.8 Existence of Separating and Supporting Hyperplanes.- 2.9 Convex Cones.- 2.10 Basic Solutions to Linear Equalities.- 2.11 Faces of Polyhedral Convex Sets: Extreme Points, Facets, and Edges.- 2.12 Extreme Point Representation for Polyhedral Convex Sets.- 2.13 Directions for Polyhedral Convex Sets.- 2.14 Combined Extreme Point and Extreme Direction Representation for Polyhedral Convex Sets.- 2.15 Resolution of Convex Polyhedra..- 2.16 Simplexes.- 2.18 Linear Functionals.- 3. Introduction to Linear Programming.- 3.1 The Canonical Form of a Linear Programming Problem.- 3.2 A Graphical Solution to the Linear Programming Problem.- 3.3 The Standard Form of a Linear Programming Problem.- 3.4 Properties of the Feasible Region.- 3.5 Existence and Location of Finite Optimal Solutions.- 3.6 Basic Feasible and Extreme Point Solutions to the Linear Programming Problem.- 3.7 Solutions and Requirements Spaces.- 4. Duality Theory.- 4.1 The Symmetric Dual.- 4.2 Unsymmetric Duals.- 4.3 Duality Theorems.- 5. The Theory of Linear Programming.- 5.1 Finding Primal Basic Feasible Solutions.- 5.2 The Reduced Primal Problem.- 5.3 The Primal Optimality Criterion.- 5.4 Constructing the Dual Solution.- 5.5 The Primal Simplex Method.- 5.6 Degenerate Basic Feasible Solutions.- 5.7 Unbounded Solutions Reexamined.- 5.8 Multiple Optimal Solutions.- 6. Duality Theory Revisited.- 6.1 The Geometry of Duality and Optimality.- 6.2 Lagrangian Saddle Points and Primal Optimality.- 7. Computational Aspects of Linear Programming.- 7.1 The Primal Simplex Method Reexamined.- 7.2 Improving a Basic Feasible Solution.- 7.3 The Cases of Multiple Optimal, Unbounded, and Degenerate Solutions.- 7.4 Summary of the Primal Simplex Method.- 7.5 Obtaining the Optimal Dual Solution From the Optimal Primal Matrix.- 8. One-Phase, Two-Phase, and Composite Methods of Linear Programming.- 8.1 Artificial Variables.- 8.2 The One-Phase Method.- 8.3 Inconsistency and Redundancy.- 8.4 Unbounded Solutions to the Artificial Problem.- 8.5 The Two-Phase Method.- 8.6 Obtaining the Optimal Primal Solution from the Optimal Dual Matrix.- 8.7 The Composite Simplex Method.- 9. Computational Aspects of Linear Programming: Selected Transformations.- 9.1 Minimizing the Objective Function.- 9.2 Unrestricted Variables.- 9.3 Bounded Variables.- 9.4 Interval Linear Programming.- 9.5 Absolute Value Functionals.- 10. The Dual Simplex, Primal-Dual, and Complementary Pivot Methods.- 10.1 Dual Simplex Method.- 10.2 Computational Aspects of the Dual Simplex Method.- 10.3 Dual Degeneracy.- 10.4 Summary of the Dual Simplex Method.- 10.5 Generating an Initial Primal-Optimal Basic Solution: The Artificial Constraint Method.- 10.6 Primal-Dual Method.- 10.7 Summary of the Primal-Dual Method.- 10.8 A Robust Primal-Dual Algorithm.- 10.9 The Complementary Pivot Method.- 11. Postoptimality Analysis I.- 11.1 Sensitivity Analysis.- 11.2 Structural Changes.- 12. Postoptimality Analysis II.- 12.1 Parametric Analysis.- 12.2 The Primal-Dual Method Revisited.- 13. Interior Point Methods.- 13.1 Optimization Over a Sphere.- 13.2 An Overview of Karmarkars Algorithm.- 13.3 The Projective Transformation T(X).- 13.4 The Transformed Problem.- 13.5 Potential Function Improvement andComputational Complexity.- 13.6 A Summary of Karmarkars Algorithm.- 13.7 Transforming a General Linear Program to Karmarkar Standard Form.- 13.8 Extensions and Modifications of Karmarkars Algorithm.- 13.9 Methods Related to Karmarkars Routine: Affine Scaling Scaling Algorithms.- 13.10 Methods Related to Karmarkars Routine: A Path-Following Following Algorithm.- 13.11 Methods Related to Karmarkars Routine: Potential Reduction Algorithms.- 13.12 Methods Related to Karmarkars Routine: A Homogeneous and Self-Dual Interior-Point, Method.- 14. Interior Point Algorithms for Solving Linear Complementarity Problems.- 14.1 Introduction.- 14.2 An Interior-Point, Path-Following Algorithm for LCP(q,M).- 14.3 An Interior-Point, Potential-Reduction Algorithm for LCP(q,M).- 14.4 A Predictor-Corrector Algorithm for Solving LCP(q,M).- 14.5 Large-Step Interior-Point Algorithms for Solving LCP(q,M).- 14.6 Related Methods for Solving LCP(q, M).- Appendix A: Updating the Basis Inverse.- Appendix B: Steepest Edge Simplex Methods.- Appendix C: Derivation of the Projection Matrix.- References.- Notation Index. Review ` ... a carefully written textbook in a clear style. It is a very informative introduction to this field and may be recommended to students as well as to everybody interested in this special field of applied mathematics. Optimization, 43 (1998) Promotional Springer Book Archives Review Quote ... a carefully written textbook in a clear style. It is a very informative introduction to this field and may be recommended to students as well as to everybody interested in this special field of applied mathematics. Optimization, 43 (1998) Details ISBN1461334365 Author M.J. Panik Short Title LINEAR PROGRAMMING MATHEMATICS Pages 498 Series Applied Optimization Language English ISBN-10 1461334365 ISBN-13 9781461334361 Media Book Format Paperback Series Number 2 Year 2012 Publication Date 2012-01-26 Imprint Springer-Verlag New York Inc. Place of Publication New York, NY Country of Publication United States DEWEY 519.72 Illustrations XII, 498 p. Subtitle Mathematics, Theory and Algorithms DOI 10.1007/978-1-4613-3434-7 AU Release Date 2012-01-26 NZ Release Date 2012-01-26 US Release Date 2012-01-26 UK Release Date 2012-01-26 Publisher Springer-Verlag New York Inc. Edition Description Softcover reprint of the original 1st ed. 1996 Alternative 9780792337829 Audience Postgraduate, Research & Scholarly We've got this At The Nile, if you're looking for it, we've got it. With fast shipping, low prices, friendly service and well over a million items - you're bound to find what you want, at a price you'll love! TheNile_Item_ID:141646098;

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