http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-2.xsd
Presenting a strong and clear relationship between theory and practice, Linear and Integer Optimization: Theory and Practice is divided into two main parts. The first covers the theory of linear and integer optimization, including both basic and advanced topics. Dantzig's simplex algorithm, duality, sensitivity analysis, integer optimization models, and network models are introduced.
Basic Concepts of Linear Optimization; The Company Dovetail; Definition of an LO-Model; Alternatives of the Standard LO-Model; Solving LO-Models Using a Computer Package; Linearizing Nonlinear Functions; Examples of Linear Optimization Models; Building and Implementing Mathematical Models; Exercises; ; LINEAR OPTIMIZATION THEORY: BASIC TECHNIQUES; ; Geometry and Algebra of Feasible Regions; The Geometry of Feasible Regions; Algebra of Feasible Regions; Feasible Basic Solutions; Exercises; ; Dantzig's Simplex Algorithm; From Vertex to Vertex to an Optimal Solution; LO-Model Reformulation; The Simplex Algorithm; Simplex Tableaus; Discussion of the Simplex Algorithm; Initialization; Uniqueness and Multiple Optimal Solutions; Models with Equality Constraints; The Revised Simplex Algorithm; Exercises; ; Duality, Feasibility,
And Optimality; The Companies Dovetail and Salmonnose; Duality and Optimality; Complementary Slackness Relations; Infeasibility and Unboundedness; Farkas' Lemma; Primal and Dual Feasible Basic Solutions; Duality and the Simplex Algorithm; The Dual Simplex Algorithm; Exercises; ; Sensitivity Analysis; Sensitivity of Model Parameters; Perturbing Objective Coefficients; Perturbing Right Hand Side Values (Nondegenerate Case); Piecewise Linearity of Perturbation Functions; Perturbation of the Technology Matrix; Sensitivity Analysis for the Degenerate Case; Shadow Prices and Redundancy of Equality Constraints; Exercises; ; Large-Scale Linear Optimization; The Interior Path; Formulation of the Interior Path Algorithm; Convergence to the Interior Path; Maintaining Feasibility; Termination and Initialization; Exercises; ; Integer Linear Optimization; Introduction; The Branch-and-Bound.
Algorithm; Linearizing Logical Forms with Binary Variables; Gomory's Cutting-Plane Algorithm; Exercises; ; Linear Network Models; LO-Models with Integer Solutions; Total Unimodularity; ILO-Models with Totally Unimodular Matrices; The Network Simplex Algorithm; Exercises; ; Computational Complexity; Introduction to Computational Complexity; Computational Aspects of Dantzig's Simplex Algorithm; The Interior Path Algorithm Has Polynomial Running Time; Computational Aspects of the Branch-and-Bound Algorithm; Exercises; ; LINEAR OPTIMIZATION PRACTICE: ADVANCED TECHNIQUES; ; Designing a Reservoir for Irrigation; The Parameters and the Input Data; Maximizing the Irrigation Area; Changing the Input Parameters of the Model; GMPL Model Code; Exercises; ; Classifying Documents by Language; Machine Learning; Classifying Documents Using Separating Hyperplanes; LO-Model for Finding Separating.
Hyperplane; Validation of a Classifier; Robustness of Separating Hyperplanes; Separation Width; Models that Maximize the Separation Width; GMPL Model Code; Exercises; ; Production Planning; A Single Product Case; Model Description; Regular Working Hours; Overtime; Allowing Overtime and Idle Time; Sensitivity Analysis; GMPL Model Code; Exercises; ; Production of Coffee Machines; Problem Setting; An LO-Model that Minimizes Backlogs; Old and Recent Backlogs; Full Week Productions; Sensitivity Analysis; GMPL Model Code; Exercises; ; Conflicting Objectives: Producing Versus Importing; Problem Description and Input Data; Modeling Two Conflicting Objectives; Pareto Optimal Point; Goal Optimization for Conflicting Objective; Soft and Hard Constraints; Sensitivity Analysis; Alternative Solution Techniques; A Comparison of the Solutions; GMPL Model Code; Exercises; ; Coalition Formation and Profit.
Distribution; The Farmers Cooperation Problem; Game Theory; Linear Production Games; How to Distribute the Total Profit Among the Farmers?; Profit Distribution for Arbitrary Numbers of Farmers; Sensitivity Analysis; Exercises; ; Minimizing Trimloss When Cutting Cardboard; Formulating the Problem; Gilmore-Gomory's Solution Algorithm; Calculating an Optimal Solution; Exercises; ; Off-Shore Helicopter Routing; Problem Description; Vehicle Routing Problems; Problem Formulation; ILO Formulation; Column Generation; Dual Values as Price Indicators for Crew Exchanges; A Round-Off Procedure for Determining an Integer Solution; Computational Experiments; Sensitivity Analysis; Exercises; ; The Catering Service Problem; Formulation of the Problem; The Transshipment Problem Formulation; Applying the Network Simplex Algorithm; Sensitivity Analysis; GMPL Model Code; Exercises; ; Appendix A.
Mathematical Proofs; Appendix B Linear Algebra; Appendix C Graph Theory; Appendix D Convexity; Appendix E Nonlinear Optimization; Appendix F Writing LO-Models in GNU MathProg (GMPL).
Includes bibliographical references (pages 639-644) and indexes.