Tables of Contents

AMPL: A Modeling Language
for Mathematical Programming

by Robert Fourer, David M. Gay, and Brian W. Kernighan

Duxbury Press / Brooks/Cole Publishing Company, 2003

Second edition now available
517 + xxi pp., ISBN 0-534-38809-4, $53.95

Chapters

 Introduction -- download in PDF (30K), gzipped postscript (15K)
1. Production Models: Maximizing Profits -- download in PDF (575K), gzipped postscript (971K)
   
2. Diet and Other Input Models: Minimizing Costs
   
3. Transportation and Assignment Models
   
4. Building Larger Models

5. Simple Sets and Indexing
   
6. Compound Sets and Indexing
   
7. Parameters and Expressions
   
8. Linear Programs: Variables, Objectives and Constraints

9. Specifying Data
   
10. Database Access

11. Modeling Commands
    
12. Display Commands
    
13. Command Scripts
    
14. Interactions with Solvers

15. Network Linear Programs
    
16. Columnwise Formulations
    
17. Piecewise-Linear Programs
    
18. Nonlinear Programs
    
19. Complementarity Problems
    
20. Integer Linear Programs

    Appendix. AMPL Reference Manual

Chapters and Sections

Chapter 1. Production Models: Maximizing Profits

1.1 A two-variable linear program

1.2 The two-variable linear program in AMPL

1.3 A linear programming model

1.4 The linear programming model in AMPL

The basic model

An improved model

Catching errors

1.5 Adding lower bounds to the model

1.6 Adding resource constraints to the model

1.7 AMPL interfaces

2.1 A linear program for the diet problem

2.2 An AMPL model for the diet problem

2.3 Using the AMPL diet model

2.4 Generalizations to blending, economics and scheduling

3.1 A linear program for the transportation problem

3.2 An AMPL model for the transportation problem

3.3 Other interpretations of the transportation model

4.1 A multicommodity transportation model

4.2 A multiperiod production model

4.3 A model of production and transportation

5.1 Unordered sets

5.2 Sets of numbers

5.3 Set operations

5.4 Set membership operations and functions

5.5 Indexing expressions

5.6 Ordered sets

Predefined sets and interval expressions

6.1 Sets of ordered pairs

6.2 Subsets and slices of ordered pairs

6.3 Sets of longer tuples

6.4 Operations on sets of tuples

6.5 Indexed collections of sets

7.1 Parameter declarations

7.2 Arithmetic expressions

7.3 Logical and conditional expressions

7.4 Restrictions on parameters

7.5 Computed parameters

7.6 Randomly generated parameters

7.7 Logical parameters

7.8 Symbolic parameters

8.1 Variables

8.2 Linear expressions

8.3 Objectives

8.4 Constraints

9.1 Formatted data: the data command

9.2 Data in lists

Lists of one-dimensional sets and parameters

Lists of two-dimensional sets and parameters

Lists of higher-dimensional sets and parameters

Combined lists of sets and parameters

9.3 Data in tables

Two-dimensional tables

Two-dimensional slices of higher-dimensional data

Higher-dimensional tables

Choice of format

9.4 Other features of data statements

Default values

Indexed collections of sets

Initial values for variables

9.5 Reading unformatted data: the read command

10.1 General principles of data correspondence

10.2 Examples of table-handling statements

10.3 Reading data from relational tables

Reading parameters only

Reading a set and parameters

Establishing correspondences

Reading other values

10.4 Writing data to relational tables

Writing rows inferred from the data specifications

Writing rows inferred from a key specification

10.5 Reading and writing the same table

Reading and writing using two table declarations

Reading and writing using the same table declaration

10.6 Indexed collections of tables and columns

Indexed collections of tables

Indexed collections of data columns

10.7 Standard and built-in table handlers

Using the standard ODBC table handler

Using the standard ODBC table handler with Access and Excel

Built-in table handlers for text and binary files

11.1 General principles of commands and options

Commands

Options

11.2 Setting up and solving models and data

Entering models and data

Solving a model

11.3 Modifying data

Resetting

Resampling

The let command

11.4 Modifying models

Removing or redefining model components

Changing the model: fix, unfix; drop, restore

Relaxing integrality

12.1 Browsing through results: the display command

Displaying sets

Displaying parameters and variables

Displaying indexed expressions

12.2 Formatting options for display

Arrangement of lists and tables

Control of line width

Suppression of zeros

12.3 Numeric options for display

Appearance of numeric values

Rounding of solution values

12.4 Other output commands

The print command

The printf command

12.5 Related solution values

Objective functions

Bounds and slacks

Dual values and reduced costs

12.6 Other display features for models and instances

Displaying model components: the show command

Displaying model dependencies: the xref command

Displaying model instances: the expand command

Generic synonyms for variables, constraints and objectives

Resource listings

12.7 General facilities for manipulating output

Redirection of output

Output logs

Limits on messages

13.1 Running scripts: include and commands

13.2 Iterating over a set: the for statement

13.3 Iterating subject to a condition: the repeat statement

13.4 Testing a condition: the if-then-else statement

13.5 Terminating a loop: break and continue

13.6 Stepping through a script

13.7 Manipulating character strings

String functions and operators

String expressions in AMPL commands

14.1 Presolve

Activities of the presolve phase

Controlling the effects of presolve

Detecting infeasibility in presolve

14.2 Retrieving results from solvers

Solve results

Solver statuses of objectives and problems

Solver statuses of variables

Solver statuses of constraints

AMPL statuses

14.3 Exchanging information with solvers via suffixes

User-defined suffixes: integer programming directives

Solver-defined suffixes: sensitivity analysis

Solver-defined suffixes: infeasibility diagnosis

Solver-defined suffixes: direction of unboundedness

Defining and using suffixes

14.4 Alternating between models

14.5 Named problems

Defining named problems

Using named problems

Displaying named problems

Defining and using named environments

15.1 Minimum-cost transshipment models

A general transshipment model

Specialized transshipment models

Variations on transshipment models

15.2 Other network models

Maximum flow models

Shortest path models

Transportation and assignment models

15.3 Declaring network models by node and arc

A general transshipment model

A specialized transshipment model

Variations on transshipment models

Maximum flow models

15.4 Rules for node and arc declarations

node declarations

arc declarations

Interaction with objective declarations

Interaction with constraint declarations

Interaction with variable declarations

15.5 Solving network linear programs

16.1 An input-output model

Formulation by constraints

A columnwise formulation

Refinements of the columnwise formulation

16.2 A scheduling model

16.3 Rules for columnwise formulations

17.1 Cost terms

Fixed numbers of pieces

Varying numbers of pieces

17.2 Common two-piece and three-piece terms

Penalty terms for "soft" constraints

Dealing with infeasibility

Reversible activities

17.3 Other piecewise-linear functions

17.4 Guidelines for piecewise-linear optimization

Forms for piecewise-linear expressions

Suggestions for piecewise-linear models

18.1 Sources of nonlinearity

Dropping a linearity assumption

Achieving a nonlinear effect

Modeling an inherently nonlinear process

18.2 Nonlinear variables

Initial values of variables

Automatic substitution of variables

18.3 Nonlinear expressions

18.4 Pitfalls of nonlinear programming

Function range violations

Multiple local optima

Other pitfalls

19.1 Sources of complementarity

A complementarity model of production economics

Complementarity for bounded variables

Complementarity for price-dependent demands

Other complementarity models and applications

19.2 Forms of complementarity constraints

19.3 Working with complementarity constraints

Related solution values

Presolve

Generic synonyms

20.1 Integer variables

20.2 Zero-one variables and logical conditions

Fixed costs

Zero-or-minimum restrictions

Cardinality restrictions

20.3 Practical considerations in integer programming

A.1 Lexical rules

A.2 Set members

A.3 Indexing expressions and subscripts

A.4 Expressions

A.4.1 Built-in functions

A.4.2 Strings and regular expressions

A.4.2 Piecewise-linear terms

A.5 Declarations of model entities

A.6 Set declarations

A.6.1 Cardinality and arity function

A.6.2 Ordered sets

A.6.3 Intervals and other infinite sets

A.7 Parameter declarations

A.7.1 Check statements

A.7.2 Infinity

A.8 Variable declarations

A.8.1 Defined variables

A.9 Constraint declarations

A.9.1 Complementarity constraints

A.10 Objective declarations

A.11 Suffix notation for auxiliary values

A.11.1 Suffix declarations

A.11.2 Statuses

A.12 Standard data format

A.12.1 Set data

A.12.2 Parameter data

A.13 Database access and tables

A.14 Command language overview

A.14.1 Options and environment variables

A.15 Redirection of input and output

A.16 Printing and display commands

A.17 Reading data

A.18 Modeling commands

A.18.1 The solve command

A.18.2 The solution command

A.18.3 The write command

A.18.4 Auxiliary files

A.18.5 Changing a model: delete, purge, redeclare

A.18.6 The drop, restore and objective commands

A.18.7 The fix and unfix commands

A.18.8 Named problems and environments

A.18.9 Modifying data: reset, update, let

A.19 Examining models

A.19.1 The show command

A.19.2 The xref command

A.19.3 The expand command

A.19.4 Generic names

A.19.5 The check command

A.20 Scripts and control flow statements

A.20.1 The for, repeat and if-then-else statements

A.20.2 Stepping through commands

A.21 Parameter declarations

A.21.1 The shell command

A.21.2 The cd command

A.21.3 The quit, exit and end commands

A.21.4 Built-in timing parameters

A.21.5 Logging

A.22 Imported functions

A.23 AMPL invocation

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