Building and Solving Mathematical Programming Models in Engineering and Science (Pure and Applied Mathematics (Wiley))

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Building and Solving Mathematical Programming Models in Engineering and Science (Pure and Applied Mathematics (Wiley))

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  • 製本 Hardcover:ハードカバー版/ページ数 546 p.
  • 言語 ENG
  • 商品コード 9780471150435
  • DDC分類 620.0015197

Full Description


Modeling is one of the most appealing areas in engineering and applied sciences. Engineers need to build models to solve real life problems. The aim of a model consists of reproducing the reality as faithfully as possible, trying to understand how the real world behaves, and obtaining the expected responses to given actions or inputs. Many types of models are used in practice, such as differential equations models, function equation models, finite difference and finite element models, mathematical programming models, etc.

Table of Contents

Preface                                            xiii
I Models 1 (70)
Linear Programming 3 (22)
Introduction 3 (1)
The Transportation Problem 4 (2)
The Production Scheduling Problem 6 (3)
Production Scheduling Problem 1 6 (3)
The Diet Problem 9 (2)
The Network Flow Problem 11 (2)
The Portfolio Problem 13 (2)
Scaffolding System 15 (3)
Electric Power Economic Dispatch 18 (7)
Exercises 21 (4)
Mixed-Integer Linear Programming 25 (22)
Introduction 25 (1)
The 0-1 Knapsack Problem 25 (2)
Identifying Relevant Symptoms 27 (2)
The Academy Problem 29 (3)
School Timetable Problem 32 (3)
Models of Discrete Location 35 (3)
Unit Commitment of Thermal Power Units 38 (9)
Exercises 43 (4)
Nonlinear Programming 47 (24)
Introduction 47 (1)
Some Geometrically Motivated Examples 47 (4)
The Postal Package Example 47 (1)
The Tent Example 48 (1)
The Lightbulb Example 48 (2)
The Surface Example 50 (1)
The Moving Sand Example 50 (1)
Some Mechanically Motivated Examples 51 (4)
The Cantilever Beam Example 51 (1)
The Two-Bar Truss Example 51 (2)
The Column Example 53 (1)
Scaffolding System 54 (1)
Some Electrically Motivated Examples 55 (7)
Power Circuit State Estimation 56 (2)
Optimal Power Flow 58 (4)
The Matrix Balancing Problem 62 (2)
The Traffic Assignment Problem 64 (7)
Exercises 69 (2)
II Methods 71 (212)
An Introduction to Linear Programming 73 (24)
Introduction 73 (1)
Problem Statement and Basic Definitions 73 (5)
Linear Programming Problem in Standard Form 78 (3)
Transformation to Standard Form 79 (2)
Basic Solutions 81 (2)
Sensitivities 83 (1)
Duality 84 (13)
Obtaining the Dual from a Primal in 85 (1)
Standard Form
Obtaining the Dual Problem 86 (1)
Duality Theorems 87 (5)
Exercises 92 (5)
Understanding the Set of All Feasible 97 (20)
Solutions
Introduction and Motivation 97 (4)
Convex Sets 101 (4)
Linear Spaces 105 (2)
Polyhedral Convex Cones 107 (2)
Polytopes 109 (1)
Polyhedra 110 (3)
General Representation of Polyhera 112 (1)
Bounded and Unbounded LPP 113 (4)
Exercises 114 (3)
Solving the Linear Programming Problem 117 (44)
Introduction 117 (1)
The Simplex Method 118 (22)
Motivating Example 118 (2)
General Description 120 (1)
Initialization Stage 121 (1)
Elemental Pivoting Operation 122 (3)
Identifying an Optimal Solution 125 (1)
Regulating Iteration 126 (1)
Detecting Unboundedness 126 (1)
Detecting Infeasibility 127 (1)
Standard Iterations Stage 127 (2)
The Revised Simplex Algorithm 129 (2)
Some Illustrative Examples 131 (9)
The Exterior Point Method 140 (21)
Initial Stage 142 (1)
Regulating Stage 143 (1)
Detecting Infeasibility and Unboundedness 144 (1)
Standard Iterations Stage 144 (2)
The EPM Algorithm 146 (2)
Some Illustrative Examples 148 (9)
Exercises 157 (4)
Mixed-Integer Linear Programming 161 (22)
Introduction 161 (1)
The Branch-Bound Method 162 (10)
Introduction 162 (1)
The BB Algorithm for MILPP 163 (1)
Branching and Processing Strategies 164 (8)
Other Mixed-Integer Liner Programming 172 (1)
Problems
The Gomory Cuts Method 172 (11)
Introduction 172 (1)
Cut Generation 173 (1)
The Gomory Cuts Algorithm for an ILPP 174 (6)
Exercises 180 (3)
Optimality and Duality in Nonlinear 183 (52)
Programming
Introduction 183 (5)
Necessary Optimality Conditions 188 (19)
Differentiability 188 (2)
Karush-Kuhn-Tucker Optimality Conditions 190 (17)
Optimality Conditions: Sufficiency and 207 (9)
Convexity
Convexity 207 (4)
Sufficiency of the Karush-Kuhn-Tucker 211 (5)
Conditions
Duality Theory 216 (5)
Practical Illustrations of Duality and 221 (5)
Separability
Centralized or Primal Approach 222 (3)
Competitive Market or Dual Approach 225 (1)
Conclusion 226 (1)
Constraint Qualifications 226 (9)
Exercises 227 (8)
Computational Methods for Nonlinear 235 (48)
Programming
Unconstrained Optimization Algorithms 236 (18)
Line Search Methods 236 (5)
Multidimensional Unconstrained 241 (13)
Optimization
Constrained Optimization Algorithms 254 (29)
Dual Methods 254 (7)
Penalty Methods 261 (8)
The Interior Point Method 269 (9)
Exercises 278 (5)
III Software 283 (86)
The GAMS Package 285 (26)
Introduction 285 (1)
Illustrative Example 286 (4)
Language Features 290 (21)
Sets 291 (2)
Scalars 293 (1)
Parameters and Tables 293 (3)
Mathematical Expression Rules in 296 (1)
Assignments
Variables 296 (3)
Equations 299 (1)
Model 299 (1)
Solve 300 (3)
Asterisk Facility 303 (1)
Display 303 (1)
Conditional Statements 304 (1)
Dynamic Sets 305 (1)
Iterative Structures 306 (3)
Writing Output Files 309 (1)
Output File: Nonlinear Equation Listing 310 (1)
Some Examples Using GAMS 311 (58)
Introduction 311 (1)
Linear Programming Examples 311 (19)
The Transportation Problem 311 (4)
Production Scheduling Problem 1 315 (2)
The Diet Problem 317 (2)
The Network Flow Problem 319 (5)
The Portfolio Problem 324 (1)
The Scaffolding System 325 (3)
Electric Power Economic Dispatch 328 (2)
Mixed-Integer LPP Examples 330 (14)
The 0-1 Knapsack Example 331 (2)
Identifying Relevant Symptoms 333 (1)
The Academy Problem 334 (3)
The School Timetable Problem 337 (1)
Models of Discrete Location 338 (3)
Unit Commitment of Thermal Power Units 341 (3)
Nonlinear Programming Examples 344 (25)
The Postal Package Example 344 (1)
The Tent Example 345 (1)
The Lightbulb Example 346 (1)
The Surface Example 346 (1)
The Moving Sand Example 347 (1)
The Cantilever Beam Example 348 (1)
The Two-Bar Truss Example 348 (2)
The Column Example 350 (1)
The Scaffolding Example 351 (2)
Power Circuit State Estimation 353 (2)
Optimal Power Flow 355 (4)
The Water Supply Network Problem 359 (2)
The Matrix Balancing Problem 361 (2)
The Traffic Assignment Problem 363 (1)
Exercises 364 (5)
IV Applications 369 (108)
Applications 371 (80)
Applications to Artificial Intelligence 371 (7)
Learning the Neural Functions 373 (5)
Applications to CAD 378 (9)
Automatic Mesh Generation 381 (6)
Applications to Probability 387 (8)
Compatibility of Conditional Probability 387 (4)
Matrices
ε Compatibility 391 (4)
Regression Models 395 (6)
Applications to Optimization Problems 401 (16)
Variational Problems 403 (7)
Optimal Control Problems 410 (7)
Transportation Systems 417 (25)
Introduction 417 (1)
Elements of a Road Transportation Network 418 (4)
The Traffic Assignment Problem 422 (7)
Side-Constrained Assignment Models 429 (3)
The Variable-Demand Case 432 (6)
Combined Distribution and Assignment 438 (4)
Short-Term Hydrothermal Coordination 442 (9)
Problem Formulation and the LR Solution 443 (4)
Procedure
Dual-Problem Solution: Multiplier 447 (1)
Updating Techniques
Economical Meaning of the Multipliers 448 (3)
Some Useful Modeling Tricks 451 (26)
Introduction 451 (1)
Some General Tricks 451 (15)
Dealing with Unrestricted Variables 452 (1)
Converting Inequalities into Equalities 453 (1)
Converting Equalities into Inequalities 454 (1)
Converting Maximization into Minimization 455 (1)
Problems
Converting Nonlinear Objective Functions 455 (1)
into Linear
Nonlinear Functions Treated as Linear 455 (3)
Functions
Linear Space as a Cone 458 (2)
Alternative Sets of Constraints 460 (2)
Dealing with Conditional Constraints 462 (1)
Dealing with Discontinuous Functions 462 (1)
Dealing with Piecewise Nonconvex Functions 463 (3)
Some GAMS Tricks 466 (11)
Assigning Values to a Matrix 466 (1)
Defining a Symmetric Matrix 467 (1)
Defining a Sparse Matrix 467 (2)
Splitting a Separable Problem 469 (1)
Adding Constraints Iteratively to a 470 (1)
Problem
Dealing with Initial and Final States 471 (1)
Performing a Sensitivity Analysis 471 (1)
Making the Model Dependent on Problem 472 (1)
States
Exercises 473 (4)
A Compatibility and Set of All Feasible 477 (40)
Solutions
The Dual Cone 478 (2)
Cone Associated with a Polyhedron 480 (3)
The T Procedure 483 (5)
Compatibility of Linear Systems 488 (3)
Solving Linear Systems 491 (3)
Applications to Several Examples 494 (23)
The Transportation Problem 494 (5)
Production Scheduling Problem 499 (6)
The Input-Output Tables 505 (2)
The Diet Problem 507 (1)
The Network Flow Problem 508 (5)
Exercises 513 (4)
B Notation 517 (16)
Bibliography 533 (8)
Index 541