9780262720274

Many science and engineering applications require the user to find solutions to systems of nonlinear constraints or to optimize a nonlinear function subject to nonlinear constraints. The field of global optimization is the study of methods to find all solutions to systems of nonlinear constraints and all global optima to optimization problems. Numerica is modeling language for global optimization that makes it possible to state nonlinear problems in a form close to the statements traditionally found in textbooks and scientific papers. The constraint-solving algorithm of Numerica is based on a combination of traditional numerical methods such as interval and local methods, and constraint satisfaction techniques. This comprehensive presentation of Numerica describes its design, functions, and implementation. It also discusses how to use Numerica effectively to solve practical problems and reports a number of experimental results. A commercial implementation of Numerica is available from ILOG under the name ILOG Numerica.

List of Tables

viii

(1)

List of Figures

ix

(2)

List of Statements

xi

(2)

Preface

xiii

1 Introduction

1

(18)

1.1 Nonlinear Programming

1

(5)

1.2 Local Methods

6

(7)

1.3 Global Methods

13

(3)

1.4 Numerica

16

(2)

1.5 Outline

18

(1)

2 A Tour of Numerica

19

(24)

2.1 Getting Started

19

(3)

2.2 Generic Constraints

22

(1)

2.3 Constants

23

(2)

2.4 Ranges

25

(1)

2.5 Input Parameters

25

(1)

2.6 Aggregation Operators

26

(2)

2.7 Functions

28

(1)

2.8 Sets

28

(2)

2.9 Unconstrained Optimization

30

(3)

2.10 Constrained Optimization

33

(1)

2.11 Local Constraint Solving

34

(2)

2.12 Local Unconstrained Optimization

36

(1)

2.13 Soft Constraints

36

(1)

2.14 Real Constants and Uncertain Data

37

(2)

2.15 Display

39

(1)

2.16 Accuracy

40

(3)

3 The Meaning of Numerica

43

(14)

3.1 Interval Analysis

43

(4)

3.2 Constraint Solving

47

(3)

3.3 Unconstrained Optimization

50

(3)

3.4 Interpretation of the Results

53

(4)

4 Modeling in Numerica

57

(18)

4.1 What Can Go Wrong in Numerica

57

(6)

4.2 Improving Numerica Statements

63

(12)

5 The Syntax of Numerica

75

(36)

5.1 Overall Structure

75

(1)

5.2 Expressions

76

(3)

5.3 The Constant Section

79

(6)

5.4 The Input Section

85

(2)

5.5 The Set Section

87

(2)

5.6 The Variable Section

89

(1)

5.7 The Function Section

90

(2)

5.8 The Body Section

92

(9)

5.9 The Display Section

101

(7)

5.10 The Pragma Section

108

(1)

5.11 Scoping Rules

109

(2)

6 The Semantics of Numerica

111

(10)

6.1 Interval Arithmetic

111

(2)

6.2 Semantics of Constraint Solving

113

(2)

6.3 Semantics of Unconstrained Minimization

115

(2)

6.4 Semantics of Constrained Minimization

117

(3)

6.5 Non-Canonical Boxes

120

(1)

7 An Implementation of Numerica

121

(20)

7.1 Overview of the Algorithm

121

(2)

7.2 Domain-Specific and Monotonic Interval Extensions

123

(1)

7.3 Constraint Solving

124

(4)

7.4 Unconstrained Optimization

128

(3)

7.5 Constrained Optimization

131

(1)

7.6 Advanced Techniques

132

(5)

7.7 An Implementation of Box Consistency

137

(4)

8 Experimental Results

141

(21)

8.1 Constraint Solving

141

(6)

8.2 Unconstrained Optimization

147

(10)

8.3 Constrained Optimization

157

(5)

Appendix 1: Syntax of Numerica

162

(8)

Appendix 2: Benchmarks

170

(33)

Bibliography

203

(4)

Index

207

What is included with this book?

The New copy of this book will include any supplemental materials advertised. Please check the title of the book to determine if it should include any access cards, study guides, lab manuals, CDs, etc.

The Used, Rental and eBook copies of this book are not guaranteed to include any supplemental materials. Typically, only the book itself is included. This is true even if the title states it includes any access cards, study guides, lab manuals, CDs, etc.

Amazon no longer offers textbook rentals. We do!

Amazon no longer offers textbook rentals. We do!

We're the #1 textbook rental company. Let us show you why.

Numerica

0262720272

Summary

Table of Contents

Supplemental Materials

Rewards Program