Algebraic Modeling Languages

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Emmanuel Fragniere. Optimization Modeling Languages

• Software for Optimization: A Survey of Trends in Mathematical Programming Systems for Operations Research and Management Science by Robert Fourer
• AMPL

Using AMPL (example)
EXAMINING MODELS AND DATA IN AMPL
AMPL tutorial
AMPL A Mathematical Programming Language at the University of Michigan Documentation by D Holmes
Using AMPL under UNIX
New AMPL commands
AMPL display and reporting
New AMPL language features
AMPL scripts
Suffixes in AMPL
Built-in suffices in AMPL
Fix bugs in AMPL
New in AMPL CHANGING THE MODEL AND DATA
CHARACTER STRINGS in AMPL
FORMAT STRINGS FOR printf AND sprintf
REGULAR EXPRESSIONS in AMPL
New in AMPL
OPTIONS_INOUT file for AMPL
AMPL documentation
Example Problems Solved By AMPL (by Feng-Tien Yu)
A short tutorial on AMPL (Postscript file)
Brief introduction into AMPL
Modeliser avec AMPL (French)
AMPL Implementation of Kruskal's Algorithm
H. Mittelmann's AMPL collection

MINLP Directives for AMPL

• GAMS

GENERAL ALGEBRAIC MODELING SYSTEM GAMS by Michael R. Bussieck & Alex Meeraus
Notes on GAMS for Optimization by Ronald L. Rardin

A Quick Tour of GAMS by by Tim Hultberg,
McCarl et al. GAMS User Guide 2003
Introduction to GAMS by Ignacio E. Grossmann
Introduction to GAMS Software by Jean-Christophe Dumont and Veronique Robichaud
Mathematical Modeling and Optimization with Applications in Finance by S. Nielsen
GAMS options
Review of optimization and Introduction to GAMS (Slides by Juha Haataja)
GAMS - The Solver Manuals
OQNLP, from Optimal Methods Inc. and OptTek Systems, Inc., is a solver for global optimization of smooth constrained problems with either all continuous variables or a mixture of discrete and continuous variables. It starts any GAMS NLP solver from a set of starting points chosen by the widely used Scatter Search software, OptQuest. It can also be used to solve any NLP problem where solver failures are common, by automating the process of choosing multiple starting points.
GAMS/BARON BARON (Branch-And-Reduce Optimization Navigator) is a computational system for solving non convex optimization problems to global optimality.
GAMS/LGO The LGO solver integrates algorithms of global and local scope.
BUILDING APPLIED GENERAL EQUILIBRIUM MODELS WITH G A M S EXAMPLES AND ADDITIONAL UTILITIES by Michiel Keyzer
A standard computable general equilibrium (CGE) model in GAMS
A list of tips and undocumented GAMS features (by McCarl)
GAMS Model and Solver Status Codes

• LINDO/LINGO

Optimization Modeling with LINGO, a new textbook by Linus Schrage
Status Codes for LINGO

• MPL (Mathematical Programming Language) is an advanced modeling system. MPL includes an algebraic modeling language that allows to create optimization models using algebraic equations.
• LPL (mathematical modeling system which can be used to build, modify, and document large mathematical models)

• AIMMS
• ALLO (Algebraic Language for Linear Optimization) is a language for conceptualization, generation and updating the linear programming models. It is very flexible with a simple grammar and easy to use.

· Mosel (Modeling Specification and Evaluation Language)

· A Modeling System for Mixed Integer Linear Programming Using XML Technologies by Kipp Martin (PDF)

• Plam - A free MILP modeling environment using lp_solve as MILP solver and SWI-Prolog

· FLOPC++ is an open source C++ class library for algebraic modelling of linear optimization problems (LP/MIP) (COIN OSI interface).

• Spreadsheet solvers

Teaching Linear Programming using Microsoft Excel Solver by Ziggy MacDonald
Spreadsheets in Economics Teaching (References)