ISBN-10:
0262720272
ISBN-13:
9780262720274
Pub. Date:
04/25/1997
Publisher:
MIT Press
Numerica: A Modeling Language for Global Optimization

Numerica: A Modeling Language for Global Optimization

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Overview

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.

Product Details

ISBN-13: 9780262720274
Publisher: MIT Press
Publication date: 04/25/1997
Series: The MIT Press
Pages: 228
Product dimensions: 7.80(w) x 8.90(h) x 0.50(d)
Age Range: 18 Years

About the Author

Pascal Van Hentenryck is Professor in the Department of Computer Science at Brown University. He is the author or editor of several MIT Press books.

Laurent Michel is Assistant Professor in the Department of Computer Science and Engineering at the University of Connecticut.

Table of Contents

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 People are Saying About This

Mark G. Wallace

This book describes an exciting development in computer science. Itdescribes a system which allows non-mathematicians to solve difficultnumerical problems using interval reasoning. The advanced intervalreasoning techniques used by *Numerica* enable it to handle non-linearconstraints and optimization with many benefits. As such this book isof considerable interest to a wide audience.

Endorsement

This book describes an exciting development in computer science. Itdescribes a system which allows non-mathematicians to solve difficultnumerical problems using interval reasoning. The advanced intervalreasoning techniques used by *Numerica* enable it to handle non-linearconstraints and optimization with many benefits. As such this book isof considerable interest to a wide audience.—Mark G. Wallace, IC-Parc, William Penney Laboratory, ImperialCollege, London

From the Publisher

"This book describes an exciting development in computer science. Itdescribes a system which allows non-mathematicians to solve difficultnumerical problems using interval reasoning. The advanced intervalreasoning techniques used by *Numerica* enable it to handle non-linearconstraints and optimization with many benefits. As such this book isof considerable interest to a wide audience." Mark G. Wallace, IC-Parc, William Penney Laboratory, ImperialCollege, London

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