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E-grāmata: Building and Solving Mathematical Programming Models in Engineering and Science

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Building and Solving Mathematical Programming Models in Engineering and SciencePalielināt
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Fundamental concepts of mathematical modeling

Modeling is one of the most effective, commonly used tools in engineering and the applied sciences. In this book, the authors deal with mathematical programming models both linear and nonlinear and across a wide range of practical applications.

Whereas other books concentrate on standard methods of analysis, the authors focus on the power of modeling methods for solving practical problems-clearly showing the connection between physical and mathematical realities-while also describing and exploring the main concepts and tools at work. This highly computational coverage includes:
* Discussion and implementation of the GAMS programming system
* Unique coverage of compatibility
* Illustrative examples that showcase the connection between model and reality
* Practical problems covering a wide range of scientific disciplines, as well as hundreds of examples and end-of-chapter exercises
* Real-world applications to probability and statistics, electrical engineering, transportation systems, and more


Building and Solving Mathematical Programming Models in Engineering and Science is practically suited for use as a professional reference for mathematicians, engineers, and applied or industrial scientists, while also tutorial and illustrative enough for advanced students in mathematics or engineering.

Recenzijas

"...plenty of examples are given...suitable for mathematical programming undergraduate courses..." (Zentralblatt Math, Vol. 1029, 2004) "I think this textbook is worth having in the college library (Interfaces, July-August 2003)

"...can be quite valuable because of its documentation of the GAMS software product...a means to learn and utilize a sophisticated linear and nonlinear programming tool." (Journal of Mathematical Psychology, 2002)

"...a welcome addition to the series of publications on mathematical programming applications to engineering problems..." Note: Review features an image of wiley.com. (IEEE Computer Applications in Power)

"...intention is to discuss the subject from an angle different from the standard, emphasizing conditions leading to well-defined problems, compatibility and uniqueness of solutions." (Mathematical Reviews, 2002i)

"...a useful and welcome addition to existing books on mathematical programmingI recommend this book..." (IIE Transactions)

"...very well suited as a professional reference or as a text for advanced mathematics or engineering courses." (Journal of Applied Mathematics and Stochastic Analysis, Vol. 15, No. 4)

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 Standard Form
85(1)
Obtaining the Dual Problem
86(1)
Duality Theorems
87(5)
Exercises
92(5)
Understanding the Set of All Feasible Solutions
97(20)
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 Problems
172(1)
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 Programming
183(52)
Introduction
183(5)
Necessary Optimality Conditions
188(19)
Differentiability
188(2)
Karush-Kuhn-Tucker Optimality Conditions
190(17)
Optimality Conditions: Sufficiency and Convexity
207(9)
Convexity
207(4)
Sufficiency of the Karush-Kuhn-Tucker Conditions
211(5)
Duality Theory
216(5)
Practical Illustrations of Duality and Separability
221(5)
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 Programming
235(48)
Unconstrained Optimization Algorithms
236(18)
Line Search Methods
236(5)
Multidimensional Unconstrained Optimization
241(13)
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 Assignments
296(1)
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 Matrices
387(4)
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 Procedure
443(4)
Dual-Problem Solution: Multiplier Updating Techniques
447(1)
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 Problems
455(1)
Converting Nonlinear Objective Functions into Linear
455(1)
Nonlinear Functions Treated as Linear Functions
455(3)
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 Problem
470(1)
Dealing with Initial and Final States
471(1)
Performing a Sensitivity Analysis
471(1)
Making the Model Dependent on Problem States
472(1)
Exercises
473(4)
A Compatibility and Set of All Feasible Solutions 477(40)
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


ENRIQUE CASTILLO, PhD, is Full Professor of Applied Mathematics at the University of Cantabria in Santander, Spain. ANTONIO J. CONEJO, PhD, is Full Professor of Electrical Engineering at the Universidad de Castilla La Mancha, Ciudad Real, Spain.

PABLO PEDREGAL, PhD, is Full Professor of Applied Mathematics at the University of Cantabria.

RICARDO GARCIA is a mathematician in the fields of optimization and operation research.

NATALIA ALGUACIL, PhD, researches optimization by decomposition techniques.
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